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R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 18 Areas of Circle, Sector and Segment

Chapter 18 – Areas of Circle, Sector and Segment Exercise Ex. 18A

Question 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 2

The
circumference of a circle is 22 cm. Find the area of its quadrant.

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 3

What
is the diameter of a circle whose area is equal to the sum of the areas of
two circles of diameters 10 cm and 24 cm?

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 4

If
the area of a circle is numerically equal to twice its circumference, then
what is the diameter of the circle?

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 5

What
is the perimeter of a square which circumscribes a circle of radius a cm?

Solution 5

Since square circumscribes a circle of radius a cm, we have

Side of the square = 2
radius of circle = 2a cm

Then, Perimeter of the square = (4
2a) = 8a cm

Question 6

Find
the length of the arc of a circle of diameter 42 cm which subtends an angle
of 60° at the centre.

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 7

Find
the diameter of the circle whose area is equal to the sum of the areas of two
circles having radii 4 cm and 3 cm.

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 8

Find
the area of a circle whose circumference is 8π.

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 9

Find
the perimeter of a semicircular protractor whose diameter is 14 cm.

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 10

Find
the radius of a circle whose perimeter and area are numerically equal.

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 11

The
radii of two circles are 19 cm and 9 cm. Find the radius of the circle which
has circumference equal to the sum of the circumferences of the two circles.

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 12

The
radii of two circles are 8 cm and 6 cm. Find the radius of the circle having
area equal to the sum of the areas of the two circles.

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 13

Find
the area of the sector of a circle having radius 6 cm and of angle 30°. [Take
π
= 3.14.]

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 14

In
a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find
the length of the arc.

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 15

The
circumferences of two circles are in the ratio 2 :
3. What is the ratio between their areas?

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 16

The
areas of two circles are in the ratio 4 : 9. What is
the ratio between their circumferences?

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 17

A
square is inscribed in a circle. Find the ratio of the areas of the circle
and the square.

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 18

The
circumference of a circle is 8 cm. Find the area of the sector whose central
angle is 72°.

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 19

A pendulum swings through an angle of 30 and describes an arc 8.8cm in length. Find the length of the pendulum

Solution 19

Length of the pendulum = radius of sector = r cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 20

The minute hand of a clock is 15cm long. Calculate the area swept by it in 20minutes. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 3.14

Solution 20

Angle described by the minute hand in 60 minutes = 360°

Angle described by minute hand in 20 minutes

                                                R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Required area swept by the minute hand in 20 minutes

                                          =Area of the sector(with r = 15 cm and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 120°)

                                                       R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 21

A sector of 56o, cut out from a circle, contains R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment. Find the radius of the circle.

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 56o and let radius is r cm

Area of sector = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Hence radius= 6cm

Question 22

The area of the sector of a circle of radius 10.5cm is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment. Find the central angle of the sector.

Solution 22

Area of the sector of circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Radius = 10.5 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 23

The perimeter of a certain sector of circle of radius 6.5cm is 31 cm. Find the area of the sector.

Solution 23

Let sector of circle is OAB

Perimeter of a sector of circle =31 cm

OA + OB + length of arc AB = 31 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

 6.5 + 6.5 + arc AB = 31 cm

  arc AB = 31 – 13

            = 18 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 24

The radius of a circle is 17.5 cm. Find the area of the sector enclosed by two radii and an arc 44cm in length.

Solution 24

Length of arc of circle = 44 cm

Radius of circle = 17.5 cm

Area of sector = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                     R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 25

Two
circular pieces of equal radii and maximum area, touching each other are cut
out from a rectangular cardboard of dimensions 14 cm x 7 cm. Find the area of
the remaining cardboard.

Solution 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 26

In
the given figure, ABCD is a square of side 4 cm. A quadrant of a circle of
radius 1 cm is drawn at each vertex of the square and a circle of diameter 2
cm is also drawn. Find the area of the shaded region. [Use π
= 3.14.]

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 27

From
a rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, a
semicircular portion with BC as diameter is cut off.  Find the area of the remaining paper.

Solution 27

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 28

In
the given figure, OABC is a square of side 7 cm. If COPB is a quadrant of a
circle with centre C find the area of the shaded region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 28

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 29

In
the given figure, three sectors of a circle of radius 7 cm, making angles of
60°, 80° and 40° at the centre are shaded. Find the area of the shaded
region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 29

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 30

In
the given figure, PQ and AB are respectively the arcs of two concentric
circles of radii 7 cm and 3.5 cm with centre O. If ∠POQ
= 30°, find the area of the shaded region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 30

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 31

In
the given figure, find the area of the shaded region, if ABCD is a square of
side 14 cm and APD and BPC are semicircles.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 31

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 32

In
the given figure, the shape of the top of a table is that of a sector of a
circle with centre 0 and ∠A0B =90°. If AO =0B
= 42 cm, then find the perimeter of the top of the table.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 32

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 33

In
the given figure, ABCD is a square of side 7 cm, DPBA and DQBC are quadrants
of circles each of the radius 7 cm. Find the area of shaded region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 33

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 34

In the given figure, AOBCA represents a quadrant of a circle of radius 3.5 cm with centre O. Calculate the area of the shaded portion.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 34

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Shaded area = (area of quadrant) – (area of DAOD)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 35

Find
the perimeter of the shaded region in the figure, if ABCD is a square of side
14 cm and APB and CPD are semicircles.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 35

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 36

In
a circle of radius 7 cm, a square ABCD is inscribed. Find the area of the
circle which is outside the square.

Solution 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 37

In
the given figure, APB and CQD are semicircles of diameter 7 cm each, while
ARC and BSD are semicircles of diameter 14 cm each. Find the

(i) perimeter,

(ii)
area of the shaded region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 38

In
the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3
cm and 7 cm respectively. Find the perimeter of shaded region. [Use π
= 3.14.]

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 38

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 39

In
the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle.
If OA = 20 cm, find the area of the shaded region. [Use π
= 3.14.]

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 40

In
the given figure, APB and AQO are semicircles and AO = OB. If the perimeter
of the figure is 40 cm, find the area of the shaded region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 41

Find
the area of a quadrant of a circle whose circumference is 44 cm.

Solution 41

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 42

In the given figure, find area of the shaded region, where ABCD is a square of side 14cm and all circles are of the same diameter.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 42

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Side of the square ABCD = 14 cm

Area of square ABCD = 14 14 = 196 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Radius of each circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of the circles = 4 area of one circle

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of shaded region = Area of square – area of 4 circles

= 196 – 154 = 42R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 43

Find
the area of the shaded region in the given figure, if ABCD is a rectangle
with sides 8 cm and 6 cm and O is the centre of the circle.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 43

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 44

A
wire is bent to form a square enclosing an area of 484 m2. Using
the same wire, a circle is formed. Find the area of the circle.

Solution 44

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 45

A
square ABCD is inscribed in a circle of radius r. Find the area of the
square.

Solution 45

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 46

The
cost of fencing a circular field at the rate of Rs.25 per metre is Rs.5500.
The field is to be ploughed at the rate of 50 paise
per m2. Find the cost of ploughing the
field.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 46

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 47

A park is in the form of a rectangle 120m by 90m. At the centre of the park there is a circular lawn as shown in the figure. The area of the park excluding the lawn is 2950R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment. Find the radius of the circular lawn. (given: R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment=3.14)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 47

Area of rectangle = (120 × 90) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                          = 10800 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of circular lawn = [Area of rectangle – Area of park excluding circular lawn]

                              = [10800 – 2950] R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 7850 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of circular lawn = 7850 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Hence, radius of the circular lawn = 50 m

Question 48

In the given figure, PQSR represents a flower bed. If OP = 21 m and OR = 14 m, find the area of the flower bed.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 48

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of flower bed = (area of quadrant OPQ)

-(area of the quadrant ORS)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 49

In the given figure O is the centre of the bigger circle, and AC is its diameter. Another circle with AB as diameter is draw. If AC = 54cm and BC = 10 cm, find the area of the shaded region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 49

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Diameter of bigger circle = AC = 54 cm

Radius of bigger circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                               R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Diameter AB of smaller circle

                              R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Radius of smaller circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of bigger circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                             = 2291. 14 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of smaller circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                              = 1521. 11 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of shaded region = area of bigger circle – area of smaller circle

                                R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 50

From
a thin metallic piece in the shape of a trapezium ABCD in which AB ‖⃦
CD and ∠BCD
= 90°, a quarter circle BFEC is removed. Given, AB = BC = 3.5 cm and DE = 2
cm, calculate the area of remaining (shaded) part of metal sheet.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 51

Find
the area of the major segment APB of a circle of radius 35 cm and ∠AOB
= 90°, as shown in the given figure.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 51

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Chapter 18 – Areas of Circle, Sector and Segment Exercise Ex. 18B

Question 1

The circumference of a circle is 39.6 cm. find its area.

Solution 1

Circumference of circle = 2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segmentr = 39.6 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 2

The
area of a circle is 98.56 cm2. Find its circumference.

Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 3

The
circumference of a circle exceeds its diameter by 45 cm. Find the
circumference of the circle.

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 4

A copper wire when bent in the form of a square encloses an area of 484 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment. The same wire is now bent in the form of a circle. Find the area enclosed by the circle.

Solution 4

Area of square = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Perimeter of square = 4 side = 4 22 = 88 cm

Circumference of circle = Perimeter of square

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 5

A wire when bent in the form of an equilateral triangle encloses an area of 121R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment. The same wire is bent to form a circle. Find the area enclosed by the circle.

Solution 5

Area of equilateral = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Perimeter of equilateral triangle = 3a = (3 22) cm

                                              = 66 cm

Circumference of circle = Perimeter of circle

2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segmentr = 66 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segmentr = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                   = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 6

The
length of a chain used as the boundary of a semicircular park is 108 m. Find
the area of the park.

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 7

The sum of the radii of two circles is 7 cm, and the difference of their circumferences is 8 cm. Find the circumferences of the circles.

Solution 7

Let the radii of circles be x cm and (7 – x) cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Circumference of the circles are 26 cm and 18 cm

Question 8

Find the area of a ring whose outer and inner radii are respectively 23 cm and 12 cm.

Solution 8

Area of outer circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                            = 1662.5 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of ring = Outer area – inner area

                 = (1662.5 – 452.5) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 9

A path of 8m width runs around the outside of a circular park whose radius is 17m. Find the area of the path.

Solution 9

Inner radius of the circular park = 17 m

Width of the path = 8 m

Outer radius of the circular park = (17 + 8)m = 25 m

Area of path = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 10

A racetrack is in the form of a ring whose inner circumference is 352m and outer circumference is 396m. Find the width and the area of the track.

Solution 10

Let r m and R m be the radii of inner circle and outer boundaries respectively.

Then, 2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segmentr = 352 and 2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentR = 396

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Width of the track = (R – r) m

                         R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area the track = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                    R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 11

A sector is cut from a circle of radius 21cm. The angle of the sector is 150o. Find the length of the arc and the area of the sector.

Solution 11

Length of the arc R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                      R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Length of arc = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of the sector = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                                      R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 12

The
area of the sector of a circle of radius 10.5 cm is 69.3 cm2. Find
the central angle of the sector.

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 13

The length of an arc of a circle, subtending an angle of 54° at the centre, is 16.5 cm. Calculate the radius, circumference and area of the circle.

Solution 13

Length of arc = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Circumference of circle = 2 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment r

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                   R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 14

The
radius of a circle with centre O is 7 cm. Two radii OA and OB are drawn at
right angles to each other. Find the areas of minor and major segments.

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 15

Find the lengths of the arcs cut off from a circle of radius 12 cm by a chord 12 cm long. Also, find the area of the minor segment. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 3.14, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentOAB is equilateral.

So, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentAOB = 60

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Length of arc BDA = (2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment 12 – arc ACB) cm

                         = (24R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment – 4R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment) cm = (20R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment) cm

                         = (20 3.14) cm = 62.8 cm

Area of the minor segment ACBA

                  R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 16

A chord 10cm long is drawn in a circle whose radius is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment. Find the areas of both the segments. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 3.13

Solution 16

Let OA = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment, OB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

And AB = 10 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentAOB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                   R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of minor segment = (area of sector OACBO) – (area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentOAB)

                                 = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 17

Find the areas of both the segments of a circle of radius 42 cm with central angle 120o. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 17

Area of sector OACBO

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of minor segment ACBA

                      R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of major segment BADB

                     R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 18

A chord of a circle of radius 30cm makes an angle of 60° at the centre of the circle. Find the areas of the minor and major segments. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 3.14, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 18

Let AB be the chord of circle of centre O and radius = 30 cm such that R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentAOB = 60°

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of the sector OACBO

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentOAB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of the minor segment ACBA

= (area of the sector OACBO) – (area of the R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentOAB)

=(471 – 389.25) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 81.75 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of the major segment BADB

= (area of circle) – (area of the minor segment)

= [(3.14 × 30 × 30) – 81.75)] R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 2744.25R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 19

In a circle of radius 10.5cm, the minor arc is one-fifth of the major arc. Find the area of the sector corresponding to the major arc.

Solution 19

Let the major arc be x cm long

Then, length of the minor arc = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Circumference = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 20

The short and long hands of a clock are 4cm and 6cm long respectively. Find the sum of distances travelled by their tips in 2days. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 3.14

Solution 20

In 2 days, the short hand will complete 4 rounds

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentDistance travelled by its tip in 2 days

=4(circumference of the circle with r = 4 cm)

= (4 × 2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment × 4) cm = 32R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment cm

In 2 days, the long hand will complete 48 rounds

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segmentlength moved by its tip

= 48(circumference of the circle with r = 6cm)

= (48 × 2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment × 6) cm = 576R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentSum of the lengths moved

= (32R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment + 576R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment) = 608R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment cm

= (608 × 3.14) cm = 1909.12 cm

Question 21

Find
the area of a quadrant of a circle whose circumference is 88 cm.

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 22

A rope by which a cow is tethered is increased from 16m to 23m. How much additional ground does it have now to graze?

Solution 22

Area of plot which cow can graze  when r = 16 m is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                                                        R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                                                        = 804.5 m2

Area of plot which cow can graze when radius is increased to 23 m

                                                                     R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Additional ground = Area covered by increased rope – old area

                        = (1662.57 – 804.5) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 858 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 23

A horse is placed for grazing inside a rectangular field 70m by 52m. It is tethered to one corner by a rope 21 m long. On how much area can it graze? How much area is left ungrazed?

Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area which the horse can graze = Area of the quadrant of radius 21 m

                                             R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area ungrazed = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                     R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 24

A horse is tethered to one corner of a field which is in the shape of an equilateral triangle of side 12m. If the length of the rope is 7m, find the area of the field which the horse cannot graze. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment. Write the answer correct to 2 places of decimal.

Solution 24

Each angle of equilateral triangle is 60

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area that the horse cannot graze is 36.68 m2

Question 25

Four cows are tethered at the four corners of a square field of side 50 m such that each can graze the maximum unshared area. What area will be left ungrazed? Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 3.14

Solution 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Ungrazed area

                    R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 26

In the given figure, OPQR is a rhombus, three of whose vertices lie on a circle with centre O. If the area of the rhombus is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment, find the radius of the circle.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

OP = OR = OQ = r

Let OQ and PR intersect at S

We know the diagonals of a rhombus bisect each other at right angle.

Therefore we have

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 27

The side of a square is 10 cm. Find (i) the area of the inscribed circle, and (ii) area of the circumscribed circle. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 3.14

Solution 27

Diameter of the inscribed circle = Side of the square = 10 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentRadius of the inscribed circle = 5 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Diameter of the circumscribed circle

= Diagonal of the square

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Radius of circumscribed circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

(i)Area of inscribed circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

(ii)Area of the circumscribed circle R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 28

If a square is inscribed in a circle, find the ratio of the areas of the circle and the square.

Solution 28

Let the radius of circle be r cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Then diagonal of square = diameter of circle = 2r cm

Area of the circle = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 29

The area of a circle inscribed in an equilateral triangle is 154 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment. Find the perimeter of the triangle. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 29

Let the radius of circle be r cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Let each side of the triangle be a cm

And height be h cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 30

The radius of the wheel of a vehicle is 42 cm. How many revolutions will it complete in 19.8 km long journey?

Solution 30

Radius of the wheel = 42 cm

Circumference of wheel =2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segmentr = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Distance travelled = 19.8 km = 1980000 cm

Number of revolutions = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 31

The wheels of the locomotive of a train are 2.1m in radius. They make 75 revolutions in one minute. Find the speed of the train in km per hour.

Solution 31

Radius of wheel = 2.1 m

Circumference of wheel = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Distance covered in one revolution = 13.2 m

Distance covered in 75 revolutions = (13.2 75) m = 990 m

= R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Distance a covered in 1 minute = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Distance covered in 1 hour = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 32

The wheels of a car make 2500 revolutions in covering a distance of 4.95 km. Find the diameter of a wheel.

Solution 32

Distance covered by the wheel in 1 revolution

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentThe circumference of the wheel = 198 cm

Let the diameter of the wheel be d cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Hence diameter of the wheel is 63 cm

Question 33

A boy is cycling in such a way that the wheels of his bicycle are making 140 revolutions per minute. If the diameter of a wheel is 60 cm, calculate the speed(in km/h) at which the boy is cycling.

Solution 33

Radius of the wheel R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Circumference of the wheel = 2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segmentr = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                                        R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Distance covered in 140 revolution

                                       R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Distance covered in one hour = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 34

The diameter of the wheels of a bus is 140cm, How many revolutions per minute do the wheels make when the bus is moving at a speed of 72.6 km per hour?

Solution 34

Distance covered by a wheel in 1minute

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Circumference of a wheel = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Number of revolution in 1 min = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 35

The diameter of the front and rear wheels of a tractor are 80cm and 2 m respectively. Find the number of revolutions that a rear wheel makes to cover the distance which the front wheel covers in 800 revolutions.

Solution 35

Radius of the front wheel = 40 cm = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Circumference of the front wheel= R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Distance moved by it in 800 revolution

                         R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Circumference of rear wheel = (2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment 1)m = (2R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment) m

Required number of revolutions = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 36

Four equal circles are described about the four corners of a square so that each touches two of the others, as shown in the figure. Find the area of the shaded region, if each of the square measures 14cm.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 36

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Each side of the square is 14 cm

Then, area of square = (14 × 14) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                               = 196 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Thus, radius of each circle 7 cm

Required area = area of square ABCD

                             -4 (area of sector with r = 7 cm, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 90°)

                    R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of the shaded region = 42 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 37

Four equal circles, each of radius 5 cm, touch each other, as shown in the figure. Find the area included between them. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 3.14.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 37

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Let A, B, C, D be the centres of these circles

Join AB, BC, CD and DA

Side of square = 10 cm

Area of square ABCD

                    R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of each sector = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                            = 19.625 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Required area = [area of sq. ABCD – 4(area of each sector)]

                     = (100 – 4 19.625) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                     = (100 – 78.5) R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 21.5 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 38

Four equal circles, each of radius a units, touch each other. Show that the area between them is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segmentsq. units.

Solution 38

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Required area = [area of square – areas of quadrants of circles]

Let the side = 2a unit and radius = a units

Area of square = (side side) = (2a 2a) sq. units

                                           R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 39

Three equal circles, each of radius of 6cm, touchone another as shown in the figure. Find the area enclosed between them. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 3.14 and R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment 

Solution 39

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Let A, B, C be the centres of these circles. Joint AB, BC, CA

Required area=(area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentABC with each side a = 12 cm)

                            -3(area of sector with r = 6, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 60°)

       R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

       R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

The area enclosed = 5.76 cm2

Question 40

If three circles of radius a each, are drawn such that each touches the other two, prove thatthe area included between them is equal to R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 40

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Let A, B, C be the centers of these circles. Join AB, BC, CA

Required area= (area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentABC with each side 2)

                               -3[area of sector with r = a cm, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 60°]

                      R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 41

In
the given figure, ABCD is a trapezium of area 24.5 cm2. If AD ∥
BC, ∠DAB
= 90°, AD =10 cm, BC = 4 cm and ABE is quadrant of a circle then find the
area of the shaded region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 41

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 42

ABCD
is a field in the shape of a trapezium, AD ∥
BC, ∠ABC
= 90° and ∠ADC
= 60°. Four sectors are formed with centres A, B, C and D, as shown in the
figure. The radius of each sector is 14 m. Find the following:

 i. total area of the four sectors,

 ii. area of
the remaining portion, given that AD = 55 m, BC = 45 m and AB = 30 m.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 42

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 43

Find
the area of the shaded region in the given figure, where a circular arc of
radius 6 cm has been drawn with vertex of an equilateral triangle of side 12
cm as centre and a sector of circle of radius 6 cm with centre B is made. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 43

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 44

In
the given figure, ABCD is a rectangle with AB = 80 cm and BC = 70 cm, ∠AED
= 90° and DE = 42 cm. A semicircle is drawn, taking BC as diameter. Find the
area of the shaded region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 44

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 45

In
the given figure, from a rectangular region ABCD with AB = 20 cm, a right
triangle AED with AE = 9 cm and DE =12 cm, is cut off. On the other end,
taking BC as diameter, a semicircle is added on outside the region: Find the
area of the shaded region. [Use π = 3.14.]

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 45

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 46

In
the given figure, 0 is the centre of the circle with AC = 24 cm, AB = 7 cm
and ∠BOD
= 90°. Find the area of shaded region. [Use π = 3.14.]

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 46

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 47

In
the given figure, a circle is inscribed in an equilateral triangle ABC of
side 12 cm. Find the radius of inscribed circle and the area of the shaded
region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 47

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 48

On
a circular table cover of radius 42 cm, a design is formed by a girl leaving
an equilateral triangle ABC in the middle, as shown in the figure. Find the
covered area of the design.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 48

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 49

The
perimeter of the quadrant of a circle is 25 cm. Find its area.

Solution 49

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 50

A
chord of a circle of radius 10 cm subtends a right angle at the centre. Find
the area of the minor segment. [Use π = 3.14.]

Solution 50

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 51

The
radius of a circular garden is 100 m. There is a road 10 m wide, running all
around it. Find the area of the road and the cost of levelling it at Rs.20 per m2.
[Use π
= 3.14.]

Solution 51

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 52

The area of an equilateral triangle is R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment.Taking each angular point as centre, circles are drawn with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles. TakeR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment.

Solution 52

Area of equilateral triangle ABC = 49R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Let a be its side

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of sector BDF = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of sector BDF = Area of sector CDE = Area of sector AEF

Sum of area of all the sectors

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentShaded area = Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentABC – sum of area of all sectors

                      R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 53

A child draws the figure of an aeroplane as shown. Here, the wings ABCD and FGHI are parallelograms, the tail DEF is an isosceles triangle, the cockpit CKI is a semicircle and CDFI is a square. In the given figure, BP R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentCD, HQ R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentFI and EL R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentDF. IF CD = 8cm, BP = HQ = 4 cm and DE = EF = 5cm, find the area of the whole figure. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 3.14. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 53

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 54

A circular disc of radius 6cm is divided into three sectors with central angles 90o, 120o and 150o. What part of the whole circle is the sector with central angle 150o? Also, calculate the ratio of the areas of the three sectors.

Solution 54

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 55

A round table cover has six equal designs as shown in the given figure. If the radius of the cover is 35cm, then find the total area of the design. Use R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 55

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

ABCDEF is a hexagon

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentR-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentAOB = 60, Radius = 35 cm

Area of sector AOB

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentAOB = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                   R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of segment APB = (641.083 = 530.425)R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 110.658R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of design (shaded area) = 6 110.658R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment= 663.948R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

                                                            = 663.95 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 56

In the given figure, PQ = 24cm, PR = 7cm and O is the centre of the circle. Find the area of the shaded region. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 3.14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 56

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

In R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentPQR, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentP = 90, PQ = 24 cm, PR = 7 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of semicircle

                    R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentPQR = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentShaded area = 245.31 – 84 = 161.31 R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 57

In the given figure, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentABC is right angled at A. find the area of the shaded region if AB = 6cm, BC = 10 cm and O is the centre of thein circle of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentABC. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 3.14.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

 

Solution 57

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

In R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentABC, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentA = 90°, AB = 6cm, BC = 10 cm

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of  ABC = R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Let r be the radius of circle of centre O

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 58

In the given figure, R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentABC is right-angled at A. Semicircles are drawn on AB, AC and BC as diameters. It is given that AB = 3cm and AC = 4cm. Find the area of the shaded region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 58

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of shaded region = Area of R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentABC + Area of semi-circle APB

+ Area of semi circle AQC – Area of semicircle BAC

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Further in R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentABC,R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentA = 90

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Adding (1), (2), (3) and subtracting (4)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 59

PQRS is a diameter of a circle of radius 6cm. The lengths PQ, QR, and RS are equal. Semicircles are drawn with PQ andQS as diameters, as shown in the given figure. If PS = 12cm, find the perimeter and area of the shaded region. Take R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment = 3.14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 59

        R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

PS = 12 cm

PQ = QR = RS = 4 cm, QS = 8 cm

Perimeter = arc PTS + arc PBQ + arc QES

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Area of shaded region = (area of the semicircle PBQ)

+ (area of semicircle PTS)-(Area of semicircle QES)

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 60

The inside perimeter of a running track shown in the figure is 400 m. The length of each of the straight portions is 90m, and the ends are semicircles. If the track is 14 m wide everywhere, find the area of the track. Also, find the length of the outer boundary of the track.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 60

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Length of the inner curved portion

= (400 – 2 90) m

= 220 m

Let the radius of each inner curved part be r

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Inner radius = 35 m, outer radius = (35 + 14) = 49 m

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And SegmentArea of the track = (area of 2 rectangles each 90 m 14 m)

+ (area of circular ring with R = 49 m, r = 35 m

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Length of outer boundary of the track

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Chapter 18 – Areas of Circle, Sector and Segment Exercise FA

Question 1

In the given figure, a square OABC
has been inscribed in the quadrant OPBQ. If OA = 20cm then the area of the
shaded region is [take
π=3.14]

  1. 214 cm2
  2. 228 cm2
  3. 242 cm2
  4. 248 cm2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 2

The diameter of a wheel is 84 cm.
How many revolutions will it make to cover 792 m?

  1. 200
  2. 250
  3. 300
  4. 350
Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 3

The area of a sector of a circle
with radius r, making an angle of x
° at the centre is

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 4

In the given figure, ABCD is a rectangle inscribed in a
circle having length 8 cm and breadth 6 cm. If
π
= 3.14 then the area of the shaded region is

  1. 264 cm2
  2. 266 cm2
  3. 272 cm2
  4. 254 cm2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 5

The circumference of a circle is 22 cm. Find its area. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 6

In
a circle of radius 21 cm, an arc subtends an angle of 60°
at the centre. Find the length of the arc.

Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 7

The minute hand of a clock is 12 cm
long. Find the area swept by it in 35 minutes.

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 8

The
perimeter of a sector of a circle radius 5.6 cm is 27.2 cm. Find the area of
the sector.

Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 9

A
chord of a circle of radius 14 cm makes right angle at the centre. Find the
area of the sector.

Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 10

In the given figure, the sectors of two concentric circles
of radii 7 cm and 3.5 cm are shown. Find the area of the shaded region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 12

The wheel of a cart is making 5 revolutions per second. If
the diameter of the wheel is 84 cm. find its speed in km per hour. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 13

OACB
is a quadrant of a circle with centre O and its radius is 3.5 cm. If OD = 2
cm, find the area of (i) the quadrant OACB (ii) the shaded region. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 14

In
the given, ABCD is a square each of whose side measures 28 cm. Find the area
of the shaded region. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 15

In
the given figure, an equilateral triangle has been inscribed in a circle of
radius 4 cm. Find the area of the shaded region.

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 16

The
minute hand of a clock is 7.5 cm long. Find the area

Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 17

A racetrack is in the form of a ring whose inner
circumference is 352 m and outer circumference is 396 m. Find the width and
the area of the track.

Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 18

A chord of circle of radius 30 cm makes an angle of 60°
at the centre of the circle. Find the area of the minor and major segment. R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 19

Four
cows are tethered at the four corners of a square field of side 50 m such
that each can graze the maximum unshared area. What area will be left ungrazed?
[Take π
= 3.14]

Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 20

A
square tank has an area of 1600 m2. There are four semicircular
plots around it. Find the cost of turfing the plots at Rs. 12.50 per m2.[Take π = 3.14]

Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Chapter 18 – Areas of Circle, Sector and Segment Exercise MCQ

Question 1

The area of a circle is 38.5 cm2. The circumference of the circle is

  1. 6.2 cm
  2. 12.2 cm
  3. 11 cm
  4. 22 cm
Solution 1

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 2

The area of a circle is 49πcm2. Its circumference is

  1. 7π cm
  2. 14π cm
  3. 21π cm
  4. 28π cm
Solution 2

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 3

The difference between the circumference and radius of a circle is 37 cm. The area of the circle is

a. 111 cm2

b. 184 cm2

c. 154 cm2

d. 259 cm2

Solution 3

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 4

The perimeter of a circular field is 242 m. The area of the field is

  1. 9317 m2
  2. 18634 m2
  3. 4658.5  m2
  4. none of these
Solution 4

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 5

On increasing the diameter of a circle by 40%, its area will be increased by

  1. 40%
  2. 80%
  3. 96%
  4. 82%
Solution 5

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 6

On decreasing the radius of circle by 30%, its area is decreased by

  1. 30%
  2. 60%
  3. 45%
  4. none of these
Solution 6

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 7

The area of a square is the same as the area of a circle. Their perimeters are in the ratio

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 7

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 8

The circumference of a circle is equal to the circumferences of two circle having diameters 36 cm and 20 cm. The radius of the new circle is

  1. 16 cm
  2. 28 cm
  3. 42 cm
  4. 56 cm
Solution 8

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 9

The area of a circle is equal to the sum of the areas of two circles of radii 24 cm and 7 cm. The diameter of the new circle is

  1. 25 cm
  2. 31 cm
  3. 50 cm
  4. 62 cm
Solution 9

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 10

If the perimeter of a square is equal to the circumference of a circle then the ratio of their areas is

  1. 4:π
  2. π:4
  3. π:7
  4. 7: π
Solution 10

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 11

If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R then

  1. R1 + R2 = R
  2. R1 + R2< R
  3. R12 + R22< R2
  4. R12 + R22 = R2
Solution 11

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 12

If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a radius R then

  1. R1 + R2 = R
  2. R1 + R2> R
  3. R1 + R2< R2
  4. none of these
Solution 12

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 13

If the circumference of a circle and the perimeter of a square are equal then

  1. area of the circle = area of the square
  2. (area of the circle) > (area of the square)
  3. (area of the circle) < (area of the square)
  4. none of these
Solution 13

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 14

The radii of two concentric circles are 19 cm and 16 cm respectively. The area of the ring enclosed by these circle is

  1. 320 cm2
  2. 330 cm2
  3. 332 cm2
  4. 340 cm2
Solution 14

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 15

The areas of two concentric circles are 1386 cm2 and 962.5 cm2. The width of the ring is

  1. 2.8 cm
  2. 3.5 cm
  3. 4.2 cm
  4. 3.8 cm
Solution 15

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 16

The circumferences of two circles are in the ratio 3:4. The ratio of their areas is

  1. 3:4
  2. 4:3
  3. 9:16
  4. 16:9
Solution 16

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 17

The area of two circles is in the ratio 9:4. The ratio of their circumference is

  1. 3:2
  2. 4:9
  3. 2:3
  4. 81:16
Solution 17

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 18

The radius of a wheel is 0.25 m. How many revolutions will it make in covering 11 km?

  1. 2800
  2. 4000
  3. 5500
  4. 7000
Solution 18

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 19

The diameter of a wheel is 40 cm. How many revolutions will it make in covering 176 m?

  1. 140
  2. 150
  3. 160
  4. 166
Solution 19

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 20

In making 1000 revolutions, a wheel covers 88 km. The diameter of the wheel is

  1. 14 m
  2. 24 m
  3. 28 m
  4. 40 m
Solution 20

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 21

The area of a sector of angle θ° of a circle with radius R is

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 21

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 22

The length of an arc of a sector of angle θ° of a circle with radius R is

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Solution 22

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 23

The length of the minute hand of a clocks is 21 cm. The area swept by the minute hand in 10 minutes is

  1. 231 cm2
  2. 210 cm2
  3. 126 cm2
  4. 252 cm2
Solution 23

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 24

A chord of a circle of radius 10 cm subtends right angles at the centre. The area of the minor segment

( given, π=3.14) is

  1. 32.5 cm2
  2. 34.5 cm2
  3. 28.5 cm2
  4. 30.5 cm2
Solution 24

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 25

In a circle of radius 21 cm, an arc subtends an angles of 60° at the centre. The length of the arc is

  1. 21 cm
  2. 22 cm
  3. 18.16 cm
  4. 23.5 cm
Solution 25

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

Question 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

  1. 120.56 cm2
  2. 124.63 cm2
  3. 118.24 cm2
  4. 130.57 cm2
Solution 26

R-s-aggarwal-and-v-aggarwal Solutions Cbse Class 10 Mathematics Chapter - Areas Of Circle Sector And Segment

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