## EXERCISE 11.3

#### Page No 223:

#### Question 1:

Find the circumference of the circles with the following radius: (Takeπ)

(a) 14 cm (b) 28 mm (c) 21 cm

#### Answer:

(a) *r* = 14 cm

Circumference = 2π*r * = 88 cm

(b) *r *= 28 mm

Circumference = 2π*r* = 176 mm

(c) *r* = 21 cm

Circumference = 2π*r* = 132 cm

#### Question 2:

Find the area of the following circles, given that:

(a) radius = 14 mm (Takeπ) (b) diameter = 49 m

(c) radius = 5 cm

#### Answer:

(a) *r* = 14 mm

Area = π*r*^{2} = 616 mm^{2}

(b) *d* = 49 m

*r *=

Area = π*r*^{2 }== 1886.5 m^{2}

(c) *r *= 5 cm

Area = π*r*^{2 }= = 78.57 cm^{2}

#### Question 3:

If the circumference of a circular sheet is 154m, find its radius. Also find the area of

the sheet. (Takeπ)

#### Answer:

Circumference = 2π*r* =154 m

Area = π*r*^{2} =

= = 1886.5 m^{2}

#### Question 4:

A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the costs of the rope, if it cost Rs 4 per meter. (Takeπ)

#### Answer:

*d *= 21 m

*r* =

Circumference = 2π*r* == 66 m

Length of rope required for fencing = 2 × 66 m = 132 m

Cost of 1 m rope = Rs 4

Cost of 132 m rope = 4 × 132 = Rs 528

#### Question 5:

From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet. (Takeπ = 3.14)

#### Answer:

Outer radius of circular sheet = 4 cm

Inner radius of circular sheet = 3 cm

Remaining area = 3.14 × 4 × 4 − 3.14 × 3 × 3

= 50.24 − 28.26

= 21.98 cm^{2}

#### Question 6:

Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs Rs 15.( Takeπ = 3.14)

#### Answer:

Circumference = 2π*r*

Cost of 1 m lace = Rs 15

Cost of 4.71 m lace = 4.71 × 15 = Rs 70.65

#### Question 7:

Find the perimeter of the adjoining figure, which is a semicircle including its diameter.

#### Answer:

Radius = 5 cm

Length of curved part = π*r*

= 15.71 cm

Total perimeter = Length of curved part + Length of diameter

= 15.71 + 10 = 25.71 cm

#### Question 8:

Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is Rs 15/m^{2}. (Take π = 3.14)

#### Answer:

Diameter = 1.6 m

Radius = 0.8 m

Area = 3.14 × 0.8 × 0.8

= 2.0096 m^{2}

Cost for polishing 1 m^{2} area = Rs 15

Cost for polishing 2.0096 m^{2} area = 15 × 2.0096 = 30.14

Therefore, it will cost Rs 30.14 for polishing such circular table.

#### Question 9:

Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square? (Takeπ)

#### Answer:

Circumference = 2π*r* = 44 cm

*r* = 7 cm

Area = π*r*^{2}

If the wire is bent into a square, then the length of each side would be =

Area of square = (11)^{2} = 121 cm^{2}

Therefore, circle encloses more area.

#### Question 10:

From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed (as shown in the following figure). Find the area of the remaining sheet. (Takeπ)

#### Answer:

Area of bigger circle == 616 cm^{2}

Area of 2 small circles = 2 × π*r*^{2} = 77 cm^{2}

Area of rectangle = Length × Breadth = 3 × 1 = 3 cm^{2}

Remaining area of sheet = 616 − 77 − 3 = 536 cm^{2}

#### Page No 224:

#### Question 11:

A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet? (Take π = 3.14)

#### Answer:

Area of square-shaped sheet = (Side)^{2} = (6)^{2} = 36 cm^{2}

Area of circle = 3.14 × 2 × 2 = 12.56 cm^{2}

Remaining area of sheet = 36 − 12.56 = 23.44 cm^{2}

#### Question 12:

The circumference of a circle is 31.4 cm. Find the radius and the area of the circle? (Take π = 3.14)

#### Answer:

Circumference = 2π*r* = 31.4 cm

2 × 3.14 × *r* = 31.4

*r* = 5 cm

Area = 3.14 × 5 × 5 = 78.50 cm^{2}

#### Question 13:

A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? (π = 3.14)

#### Answer:

Radius of flower bed = 33 m

Radius of flower bed and path together = 33 + 4 = 37 m

Area of flower bed and path together = 3.14 × 37 × 37 = 4298.66 m^{2}

Area of flower bed = 3.14 × 33 × 33 = 3419.46 m^{2}

Area of path = Area of flower bed and path together − Area of flower bed

= 4298.66 − 3419.46 = 879.20 m^{2}

#### Question 14:

A circular flower garden has an area of 314 m^{2}. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden? (Take π = 3.14)

#### Answer:

Area = π*r*^{2} = 314 m^{2}

3.14 × *r*^{2} = 314

*r*^{2} = 100

*r* = 10 m

Yes, the sprinkler will water the whole garden.

#### Question 15:

Find the circumference of the inner and the outer circles, shown in the adjoining figure? (Take π = 3.14)

#### Answer:

Radius of outer circle = 19 m

Circumference = 2π*r* = 2 × 3.14 × 19 = 119.32 m

Radius of inner circle = 19 − 10 = 9 m

Circumference = 2π*r *= 2 × 3.14 × 9 = 56.52 m

#### Question 16:

How many times a wheel of radius 28 cm must rotate to go 352 m?

(Take π )

#### Answer:

*r* = 28 cm

Circumference = 2π*r* = = 176 cm

Number of rotations =

Therefore, it will rotate 200 times.

#### Question 17:

The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour. (Take π = 3.14)

#### Answer:

Distance travelled by the tip of minute hand = Circumference of the clock

= 2π*r* = 2 × 3.14 × 15

= 94.2 cm