# R S AGGARWAL AND V AGGARWAL Solutions Mathematics Class 10 Chapter 19 Volume and Surface Areas of Solids

## Chapter 19 – Volume and Surface Areas of Solids Exercise Ex. 19A

Question 1

Two
cubes each of volume 27 cm’ are joined end to end to form a solid. Find the
surface area of the resulting cuboid.

Solution 1

Question 2

Solution 2

Question 3

If
the total surface area of a solid hemisphere is 462 cm2, find its
volume.

Solution 3

Question 4

A
5-m-wide cloth is used to make a conical tent of base diameter 14 m and
height 24 m. Find the cost of cloth used at the rate of Rs. 25 per metre.

Solution 4

Question 5

If
the volumes of two cones are in the ratio of 1: 4 and their diameters are in
the ratio of 4 : 5, find the ratio of their heights.

Solution 5

Question 6

The
slant height of a conical mountain is 2.5 km and the area of its base is 1.54
km2. Find the height of the mountain.

Solution 6

Question 7

The
sum of the radius of the base and the height of a solid cylinder is 37
metres. If the total surface area of the cylinder be 1628 sq metres, find its
volume.

Solution 7

Question 8

The
surface area of a sphere is 2464 cm2. If its radius be doubled,
what will be the surface area of the new sphere?

Solution 8

Question 9

A
military tent of height 8.25 m is in the form of a right circular cylinder of
base diameter 30 m and height 5.5 in surmounted by a right circular cone of
same base radius. Find the length of canvas used in making the tent, if the
breadth of the canvas is 1.5 m.

Solution 9

s

Question 10

A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Find the cost of cloth required to make the tent at the rate of Rs.80 per square meter. Take

Solution 10

Radius of the cylinder = 14 m

And its height = 3 m

Radius of cone = 14 m

And its height = 10.5 m

Let l be the slant height

Curved surface area of tent

= (curved area of cylinder + curved surface area of cone)

Hence, the curved surface area of the tent = 1034

Cost of canvas = Rs.(1034 × 80) = Rs. 82720

Question 11

A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and the slant height of the conical portion is 53 m, find the area of canvas needed to make the tent. Take .

Solution 11

For the cylindrical portion, we have radius = 52.5 m and height = 3 m

For the conical portion, we have radius = 52.5 m

And slant height = 53 m

Area of canvas = 2rh + rl = r(2h + l)

Question 12

A rocket is in the form of a circular cylinder closed at the lower end and a cone of the same radius is attached to the top. The radius of the cylinder is 2.5m, its height of 21 m and the slant height of the cone is 8 m. Calculate the total surface area of the rocket.

Solution 12

Radius o f cylinder = 2.5 m

Height of cylinder = 21 m

Slant height of cone = 8 m

Radius of cone = 2.5 m

Total surface area of the rocket = (curved surface area of cone

+ curved surface area of cylinder + area of base)

Question 13

A
solid is in the shape of a cone surmounted on a hemisphere, the radius of
each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find
the volume of the solid.

Solution 13

Question 14

A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

Solution 14

Height of cone = h = 24 cm

Total surface area of toy

Question 15

A
toy is in the shape of a cone mounted on a hemisphere of same base radius. If
the volume of the toy is 231 cm3 and its diameter is 7 cm, find
the height of the toy.

Solution 15

Question 16

A
cylindrical container of radius 6 cm and height 15 cm is filled with ice-cream.
The whole ice-cream has to be distributed to 10 children in equal cones with
hemispherical tops. If the height of the conical portion is 4 times the

Solution 16

Question 17

A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder. The diameter of the hemisphere is 21 cm and the total height of the vessel is 14.5 cm. Find its capacity.

Solution 17

Radius of hemisphere = 10.5 cm

Height of cylinder = (14.5 10.5) cm = 4 cm

Radius of cylinder = 10.5 cm

Capacity = Volume of cylinder + Volume of hemisphere

Question 18

A
toy is in the form of a cylinder with hemispherical ends. If the whole length
of the toy is 90 cm and its diameter is 42 cm, find the cost of painting the
toy at the rate of 70 paise per sq cm.

Solution 18

Question 19

A
medicine capsule is in the shape of a cylinder with two hemispheres stuck to
each of its ends. The length of the entire capsule is 14 mm and the diameter
of the capsule is 5 mm. Find its surface area.

Solution 19

Question 20

A wooden article was made by scooping out a hemisphere from each end of a cylinder, as shown in the figure. If the height of the cylinder is 20 cm and its base is of diameter 7 cm, find the total surface area of the article when it is ready.

Solution 20

Height of cylinder = 20 cm

And diameter = 7 cm and then radius = 3.5 cm

Total surface area of article

= (lateral surface of cylinder with r = 3.5 cm and h = 20 cm)

Question 21

A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 21. cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and its height is 9.8 cm, find the volume of the water left in the tub.

Solution 21

And height of cylinder

Radius of cone r = 2.1 cm

And height of cone

Volume of water left in tub

= (volume of cylindrical tub – volume of solid)

Question 22

From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8cm and of base radius 6 cm, is hollowed out. Find the volume of the remaining solid. Also, find the total surface area of the remaining solid. Take = 3.14

Solution 22

(i)Radius of cylinder = 6 cm

Height of cylinder = 8 cm

Volume of cylinder

Volume of cone removed

(ii)Surface area of cylinder = 2 = 2× 6 × 8

Question 23

From
a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of
the same height and same diameter is hollowed out. Find the total surface
area of the remaining solid.

Solution 23

Question 24

From
a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical
holes each of radius 2.1 cm and height 4 cm are cut off. Find the volume of
the remaining solid.

Solution 24

Question 25

Solution 25

Question 26

A spherical glass vessel has a cylindrical neck 7 cm long and 4 cm in diameter. The diameter of the spherical part is 21 cm. Find the quantity of water it can hold. Use = .

Solution 26

Diameter of spherical part of vessel = 21 cm

Question 27

The adjoining figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Find the volume of the solid.

Solution 27

Height of cylinder = 6.5 cm

Height of cone =

=

Volume of solid = Volume of cylinder + Volume of cone

+ Volume of hemisphere

Question 28

From
a cubical piece of wood of side 21 cm, a hemisphere is carved out in such a
way that the diameter of the hemisphere is equal to the side of the cubical
piece. Find the surface area and volume of the remaining piece.

Solution 28

Question 29

A cubical block of side 10
cm is surmounted by a hemisphere. What is the largest diameter that the
hemisphere can have? Find the cost of painting the total surface area of the
solid so formed, at the rate of Rs.5 per 100 sq cm. [Use π
= 3.14.]

Solution 29

Question 30

A
toy is in the shape of a right circular cylinder with a hemisphere on one end
and a cone on the other. The radius and height of the cylindrical part are 5
cm and 13 cm respectively. The radii of the hemispherical and the conical
parts are the same as that of the cylindrical part. Find the surface area of
the toy, if the total height of the toy is 30 cm.

Solution 30

Question 31

The
inner diameter of a glass is 7 cm and it has a raised portion in the bottom
in the shape of a hemisphere, as shown in the figure. If the height of the
glass is 16 cm, find the apparent capacity and the actual capacity of the glass.

Solution 31

Question 32

A
wooden toy is in the shape of a cone mounted on a cylinder, as shown in the
figure. The total height of the toy is 26 cm, while the height of the conical
part is 6 cm. The diameter of the base of the conical part is 5 cm and that
of the cylindrical part is 4 cm. The conical part and the cylindrical part are
respectively painted red and white. Find the area to be painted by each of
these colours.

Solution 32

## Chapter 19 – Volume and Surface Areas of Solids Exercise Ex. 19B

Question 1

The
dimensions of a metallic cuboid are 100 cm x 80 cm x 64 cm. It is melted and
recast into a cube. Find the surface area of the cube.

Solution 1

Question 2

A
cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A
child reshapes it in the form of a sphere. Find the diameter of the sphere.

Solution 2

Question 3

Metallic
spheres of radii 6 cm, 8 cm and 10 cm respectively are melted to form a
single solid sphere. Find the radius of the resulting sphere.

Solution 3

Question 4

A solid metal cone with radius of base 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each. Find the number of balls thus formed.

Solution 4

Radius of the cone = 12 cm and its height = 24 cm

Volume of cone =

Question 5

The radii of internal and external surfaces of a hollow spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.

Solution 5

Question 6

The internal and external diameters of a hollow hemispherical shell are 6 cm and 10 cm respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.

Solution 6

Hence, height of the cone = 4 cm

Question 7

A
copper rod of diameter 2 cm and length 10 cm is drawn into a wire of uniform
thickness and length 10 m. Find the Thickness of the wire.

Solution 7

Question 8

A hemispherical bowl of internal diameter 30cm contains some liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter 5 cm and height 6 cm. Find the number of bottles necessary to empty the bowl.

Solution 8

Inner radius of the bowl = 15 cm

Volume of liquid in it =

Radius of each cylindrical bottle = 2.5 cm and its height = 6 cm

Volume of each cylindrical bottle

Required number of bottles =

Hence, bottles required = 60

Question 9

A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.

Solution 9

Let the number of cones formed be n, then

Hence, number of cones formed = 504

Question 10

A spherical cannon ball 28 cm in diameter is melted and recast into right circular conical mould, base of which is 35 cm in diameter. Find the height of the cone.

Solution 10

Radius of the cannon ball = 14 cm

Volume of cannon ball =

Let the height of cone be h cm

Volume of cone =

Hence, height of the cone = 35.84 cm

Question 11

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5cm and 2 cm. Find the radius of third ball.

Solution 11

Let the radius of the third ball be r cm, then,

Volume of third ball = Volume of spherical ball volume of 2 small balls

Question 12

A spherical shell of lead whose external and internal diameters are respectively 24 cm and 18 cm, is melted ad recast into a right circular cylinder 37 cm high. Find the diameter of the base of the cylinder.

Solution 12

External radius of shell = 12 cm and internal radius = 9 cm

Volume of lead in the shell =

Let the radius of the cylinder be r cm

Its height = 37 cm

Volume of cylinder =

Hence diameter of the base of the cylinder = 12 cm

Question 13

A hemisphere of lead of radius 9 cm is cast intoa right circular cone of height 72 cm. Find the radius of the base of the cone.

Solution 13

Volume of hemisphere of radius 9 cm

Volume of circular cone (height = 72 cm)

Volume of cone = Volume of hemisphere

Hence radius of the base of the cone = 4.5 cm

Question 14

A spherical ball of diameter 21 cm is melted and recast into cubes, each of side 1 cm. Find the number of cubes so formed.

Solution 14

Diameter of sphere = 21 cm

Volume of sphere =  =

Volume of cube = a3 = (1 1 1)

Let number of cubes formed be n

Volume of sphere = n Volume of cube

Hence, number of cubes is 4851.

Question 15

Solution 15

Volume of sphere (when r = 1 cm) =  =

Volume of sphere (when r = 8 cm) =  =

Let the number of balls = n

Question 16

A solid sphere of radius 3cm is melted and then cast into small spherical balls, each of diameter 0.6 cm. Find the number of small balls so obtained.

Solution 16

Radius of sphere = 3 cm

Volume of sphere =

Volume of small sphere =

Let number of small balls be n

Hence, the number of small balls = 1000.

Question 17

The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of the wire.

Solution 17

Diameter of sphere = 42 cm

Volume of sphere =

Diameter of cylindrical wire = 2.8 cm

Volume of cylindrical wire =

Volume of cylindrical wire = volume of sphere

Hence length of the wire 63 m.

Question 18

The diameter of a copper sphere is 18 cm. It is melted and drawn into a long wire of uniform cross section. If the length of the wire is 108 m, find its diameter.

Solution 18

Diameter of sphere = 18 cm

Length of wire = 108 m = 10800 cm

Let the radius of wire be r cm

But the volume of wire = Volume of sphere

Hence the diameter = 2r = (0.3 2) cm = 0.6 cm

Question 19

A
hemispherical bowl of internal radius 9 cm is full of water. Its contents are
emptied into a cylindrical vessel of internal radius 6 cm. Find the height of
water in the cylindrical vessel.

Solution 19

Question 20

Solution 20

Question 21

The
rain water from a roof of 44 m x 20 m drains into a cylindrical tank having
diameter of base 4 m and height 3.5 m. If the tank is just full, find the
rainfall in cm.

Solution 21

Question 22

Solution 22

Question 23

A
solid right circular cone of height 60 cm and radius 30 cm is dropped in a
right circular cylinder full of water, of height 180 cm and radius 60 cm.
Find the volume of water left in the cylinder, in cubic metres.

Solution 23

Question 24

Water
is flowing through a cylindrical pipe of internal diameter 2 cm, into a
cylindrical tank of base radius 40 cm, at the rate of 0.4 m per second.
Determine the rise in level of water in the tank in half an hour.

Solution 24

Question 25

Water
is flowing at the rate of 6 km/hr through a pipe of diameter 14 cm into a
rectangular tank which is 60 m long and 22 m wide. Determine the time in
which the level of water in the tank will rise by 7 cm.

Solution 25

Question 26

Water
in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/hr. How
much area will it irrigate in 10 minutes if 8 cm of standing water is needed
for irrigation?

Solution 26

Question 27

A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field which is 12 m in diameter and 2.5 m deep. If water flows through the pipe at the rate of 3.6 km/h, in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate ofRs. 0.07. use

Solution 27

Height of cylindrical tank = 2.5 m

Its diameter = 12 m, Radius = 6 m

Volume of tank =

Water is flowing at the rate of 3.6 km/ hr = 3600 m/hr

Diameter of pipe = 25 cm, radius = 0.125 m

Volume of water flowing per hour

Question 28

Water
running in a cylindrical pipe of inner diameter 7 cm, is collected in a
container at the rate of 192.5 litres per minute. Find the rate of flow of
water in the pipe in km/hr.

Solution 28

Question 29

150
spherical marbles, each of diameter 14 cm, are dropped in a cylindrical
vessel of diameter 7 cm containing some water, which are completely immersed
in water. Find the rise in the level of water in the vessel.

Solution 29

Question 30

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm, containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.

Solution 30

Let the number of marbles be n

n volume of marble = volume of rising water in beaker

Question 31

In
a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken
out of it is spread all around to a width of 5 m to form an embankment. Find
the height of the embankment. What value of the villagers is reflected here?

Solution 31

Question 32

In
a corner of a rectangular field with dimensions 35 m x 22 m, a well with 14 m
inside diameter is dug 8 m deep. The earth dug out is spread evenly over the
remaining part of the field. Find the rise in the level of the field.

Solution 32

Question 33

A
copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm
and diameter 49 cm to cover its whole surface. Find the length and the volume
of the wire. If the density of copper be 8.8 g per cu-cm, find the weight of
the wire.

Solution 33

Question 34

A
right triangle whose sides are 15 cm and 20 cm (other than hypotenuse), is
made to revolve about its hypotenuse. Find the volume and surface area of the
double cone so formed. (Choose value of it as found appropriate)

Solution 34

## Chapter 19 – Volume and Surface Areas of Solids Exercise Ex. 19C

Question 1

A
drinking glass is in the shape of a frustum of a cone of height 14 cm. The
diameters of its two circular ends are 16 cm and 12 cm. Find the capacity of
the glass.

Solution 1

Question 2

The
radii of the circular ends of a solid frustum of a cone are 18 cm and 12 cm
and its height is 8 cm. Find its total surface area. [Use π
= 3.14.]

Solution 2

Question 3

A
metallic bucket, open at the top, of height 24 cm is in the form of the
frustum of a cone, the radii of whose lower and upper circular ends are 7 cm
and 14 cm respectively. Find

(i) the volume of water which can
completely fill the bucket;

(ii) the
area of the metal sheet used to make the bucket.

Solution 3

Question 4

A
container, open at the top, is in the form of a frustum of a cone of height
24 cm with radii of its lower and upper circular ends as 8 cm and 20 cm
respectively. Find the cost of milk which can completely fill the container
at the rate of Rs. 21 per litre.

Solution 4

Question 5

A
container, open at the top and made up of metal sheet, is in the form of a
frustum of a cone of height 16 cm with diameters of its lower and upper ends
as 16 cm and 40 cm respectively. Find the cost of metal sheet used to make
the container, if it costs Rs. 10 per 100 cm2.

Solution 5

Question 6

The radii of the circular ends of a solid frustum of a cone are 33cm and 27 cm, and its slant height is 10 cm. Find its capacity and total surface area. Take .

Solution 6

Here R = 33 cm, r = 27 cm and l = 10 cm

Capacity of the frustum

Total surface area =

Question 7

A bucket is in the form of a frustum of a cone. Its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm, respectively. Find how many litres of water can the bucket hold. Take

Solution 7

Height = 15 cm, R = and

Capacity of the bucket =

Quantity of water in bucket = 28.49 litres

Question 8

A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the bucket if the cost of metal sheet used is Rs. 15 per . Use

Solution 8

R = 20 cm, r = 8 cm and h = 16 cm

Total surface area of container =

Cost of metal sheet used =

Question 9

A bucket made up of a metal sheet is in the form of frustum of a cone. Its depth is 24 cm and the diameters of the top and bottom are 30 cm and 10cm respectively. Find the cost of milk which can completely fill the bucket at the rate of Rs. 20 per litre and the cost of metal sheet used if it costs Rs. 10 per 100

Solution 9

R = 15 cm, r = 5 cm and h = 24 cm

(i)Volume of bucket =

Cost of milk = Rs. (8.164 20) = Rs. 163.28

(ii)Total surface area of the bucket

Cost of sheet =

Question 10

A
container in the shape of a frustum of a cone having diameters of its two
circular faces as 35 cm and 30 cm and vertical height 14 cm, is completely
filled with oil. If each cm’ of oil has mass 1.2 g, then find the cost of oil
in the container if it costs Rs.40 per kg.

Solution 10

Question 11

A
bucket is in the form of a frustum of a cone and it can hold 28.49 litres of
water. If the radii of its circular ends are 28 cm and 21 cm, find the height
of the bucket.

Solution 11

Question 12

The
radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm
< 14). If the volume of bucket is 5390 cm3, find the value of
r.

Solution 12

Question 13

The
radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm
and its slant height is 10 cm. Find its total surface area. [Use π
= 3.14.]

Solution 13

Question 14

A tent is made in the form of a frustum of a cone surmounted by another cone. The diameters of the base and the top of the frustum are 20 m and 6 m respectively, and the height is 24 m. If the height of the tent is 28 m and the radius of the conical part is equal to the radius of the top of the frustum, find the quantity of canvas required. Take

Solution 14

R = 10cm, r = 3 m and h = 24 m

Let l be the slant height of the frustum, then

Quantity of canvas = (Lateral surface area of the frustum)

+ (lateral surface area of the cone)

Question 15

A tent consists of a frustum of a cone, surmounted by a cone. If the diameters of the upper and lower circular ends of the frustum be 14 m and 26 m respectively, the height of the frustum be 8 m and the slant height of the surmounted conical portion be 12mm, find the area of the canvas required to make the tent. (Assume that the radii of the upper circular ends of the frustum and the base of the surmounted conical portion are equal.)

Solution 15

ABCD is the frustum in which upper and lower radii are EB = 7 m and FD = 13 m

Height of frustum= 8 m

Slant height of frustum

Radius of the cone = EB = 7 m

Slant height of cone = 12 m

Surface area of canvas required

Question 16

The
perimeters of the two circular ends of a frustum of a cone are 48 cm and 36
cm. If the height of the frustum is 11 cm, find its volume and curved surface
area.

Solution 16

Question 17

A solid cone of base radius 10 cm is cut into two parts through the midpoint of its height, by a plane parallel to its base. Find the ratio of the volumes of the two parts of the cone.

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

A
fez, the cap used by the Turks, is shaped like the frustum of a cone. If its
radius on the open side is 10 cm, radius at the upper base is 4 cm and its
slant height is 15 cm, find the area of material used for making it.

Solution 20

Question 21

An
oil funnel made of tin sheet consists of a 10 cm long cylindrical portion
attached to a frustum of a cone. If the total height is 22 cm, diameter of
the cylindrical portion is 8 cm and the diameter of the top of the funnel is
18 cm, find the area of the tin sheet requited to make the funnel.

Solution 21

## Chapter 19 – Volume and Surface Areas of Solids Exercise Ex. 19D

Question 1

A
river 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km/hr. Find the
amount of water (in cubic metres) that runs into the sea per minute.

Solution 1

Question 2

The
volume of a cube is 729 cm3. Find its surface area.

Solution 2

Question 3

How
many cubes of 10 cm edge can be put in a cubical box of 1 m edge?

Solution 3

Question 4

Three
cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted
and formed into a single cube. Find the edge of the new cube formed.

Solution 4

Question 5

Five
identical cubes, each of edge 5 cm, are placed adjacent to each other. Find
the volume of the resulting cuboid.

Solution 5

Question 6

The
volumes of two cubes are in the ratio 8 : 27. Find the ratio of their surface
areas.

Solution 6

Question 7

Solution 7

Question 8

The
ratio between the radius of the base and the height of a cylinder is 2 : 3.
If the volume of the cylinder is 12936 cm3, find the radius of the
base of the cylinder.

Solution 8

Question 9

The
radii of two cylinders are in the ratio of 2 : 3 and their heights are in the
ratio of 5 : 3. Find the ratio of their volumes.

Solution 9

Question 10

66
cubic cm of silver is drawn into a wire 1 mm in diameter. Calculate the
length of the wire in metres.

Solution 10

Question 11

If
the area of the base of a right circular cone is 3850 cm2 and its
height is 84 cm, find the slant height of the cone.

Solution 11

Question 12

A
cylinder with base radius 8 cm and height 2 cm is melted to form a cone of
height 6 cm. Calculate the radius of the base of the cone.

Solution 12

Question 13

A
right cylindrical vessel is full of water. How many right cones having the
same radius and height as those of the right cylinder will be needed to store
that water?

Solution 13

Question 14

The
volume of a sphere is 4851 cm3. Find its curved surface area.

Solution 14

Question 15

The
curved surface area of a sphere is 5544 cm3. Find its volume.

Solution 15

Question 16

The
surface areas of two spheres are in the ratio of 4 : 25. Find the ratio of
their volumes.

Solution 16

Question 17

A
solid metallic sphere of radius 8 cm is melted and recast into spherical
balls each of radius 2 cm. Find the number of spherical balls obtained.

Solution 17

Question 18

How
many lead shots each 3 mm in diameter can be made from a cuboid of dimensions
9 cm x 11 cm x 12 cm?

Solution 18

Question 19

A
metallic cone of radius 12 cm and height 24 cm is melted and made into
spheres of radius 2 cm each. How many spheres are formed?

Solution 19

Question 20

A
hemisphere of lead of radius 6 cm is cast into a right circular cone of
height 75 cm. Find the radius of the base of the cone.

Solution 20

Question 21

A
copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find
the length of the wire.

Solution 21

Question 22

The
radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm
respectively. Find the slant height of the frustum.

Solution 22

Question 23

Find
the ratio of the volume of a cube to that of a sphere which will fit inside
it.

Solution 23

Question 24

Find
the ratio of the volumes of a cylinder, a cone and a sphere, if each has the
same diameter and same height?

Solution 24

Question 25

Two
cubes each of volume 125 cm3 are joined end to end to form a
solid. Find the surface area of the resulting cuboid.

Solution 25

Question 26

Three
metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast
into a single large cube. Find the edge of the new cube formed.

Solution 26

Question 27

A
solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical
wire of uniform width. If the length of the wire is 12 m, find its width.

Solution 27

Question 28

A
5-m-wide cloth is used to make a conical tent of base diameter 14 m and
height 24 m. Find the cost of cloth used, at the rate of Rs. 25 per metre.

Solution 28

Question 29

A
wooden toy was made by scooping out a hemisphere of same radius from each end
of a solid cylinder. If the height of the cylinder is 10 cm and its base is
of radius 3.5 cm, find the volume of wood in the toy.

Solution 29

Question 30

Solution 30

Question 31

A
hollow sphere of external and internal diameters 8 cm and 4 cm respectively
is melted into a solid cone of base diameter 8 cm. Find the height of the
cone.

Solution 31

Question 32

A
bucket of height 24 cm is in the form of frustum of a cone whose circular
ends are of diameter 28 cm and 42 cm. Find the cost of milk at the rate of Rs.
30 per litre, which the bucket can hold.

Solution 32

Question 33

The
interior of a building is in the form of a right circular cylinder of
diameter 4.2 m and height 4 m surmounted by a cone of same diameter. The
height of the cone is 2.8 m. Find the outer surface area of the building.

Solution 33

Question 34

A
metallic solid right circular cone is of height 84 cm and the radius of its
base is 21 cm. It is melted and recast into a solid sphere. Find the diameter
of the sphere.

Solution 34

Question 35

A
toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same
radius. The total height of the toy is 15.5 cm. Find the total surface area
of the toy.

Solution 35

Question 36

If
the radii of the circular ends of a bucket 28 cm high, are 28 cm and 7 cm,
find its capacity and total surface area.

Solution 36

Question 37

A
bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm3
of water. The radii of the top and bottom circular ends are 20 cm and 12 cm
respectively. Find the height of the bucket. (Useπ
= 3.14.)

Solution 37

Question 38

The
radii of its lower and upper circular ends are 8 cm and 20 cm respectively.
Find the cost of metal sheet used in making the container at the rate of Rs.1.40 per cm2.

Solution 38

Question 39

Solution 39

Question 40

A
cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of
water. A solid cone of base diameter 7 cm and height 6 cm is completely
immersed in water. Find the volume of water

(i) displaced out of the cylinder

(ii) left
in the cylinder.

Solution 40

## Chapter 19 – Volume and Surface Areas of Solids Exercise FA

Question 1

Find the number of solid
spheres, each of diameter 6 cm, that could be moulded
to form a solid metallic cylinder of height 45 cm and diameter 4 cm.

Solution 1

Question 2

Two right circular
cylinders of equal volumes have their heights in the ratio 1: 2. What is the

Solution 2

Question 3

A circus tent is
cylindrical to a height of 4 m and conical above it. If its diameter is 105 m
and its slant height is 40 m, find the total area of the canvas required.

Solution 3

Question 4

The radii of the top and
bottom of a bucket of slant height 45 cm are 28 cm and 7 cm respectively.
Find the curved surface area of the bucket.

Solution 4

Question 5

A solid metal cone with
radius of base 12 cm and height 24 cm is melted to form solid spherical balls
of diameter 6 cm each. Find the number of balls formed.

Solution 5

Question 6

A hemispherical bowl of
internal diameter 30 cm is full of a liquid. This liquid is filled into
cylindrical-shaped bottles each of diameter 5 cm and height 6 cm. How many
bottles are required?

Solution 6

Question 7

A solid metallic sphere
of diameter 21 cm is melted and recast into Milan cones, each of diameter 3.5
cm and height 3 cm. Find the number of cones so formed.

Solution 7

Question 8

The diameter of a sphere
is 42 cm. it is melted and drawn into a cylindrical wire of diameter 2.8 cm.
Find the length of the wire.

Solution 8

Question 9

A drinking glass is in
the shape of frustum of a cone of height 21 cm with 6 cm and 4 cm as the
diameters of its two circular ends. Find the capacity of the glass.

Solution 9

Question 10

Two cubes, each of volume
64 cm3, are joined end to end. Find the total surface area of the
resulting cuboid.

Solution 10

Question 11

Solution 11

Question 12

A toy is in the form of
a cone mounted on a hemisphere of common base radius 7 cm. The total height
of the toy is 31 cm. Find the total surface area of the toy.

Solution 12

Question 13

A hemispherical bowl of
internal radius 9 cm is full of water. This water is to be filled in
cylindrical bottles of diameter 3 cm and height 4 cm. Find the number of
bottles needed to fill the whole water of the bowl.

Solution 13

Question 14

Solution 14

Question 15

The slant height of the
frustum of a cone is 4 cm and the perimeters (i.e., circumferences) of its
circular ends are 18 cm and 6 cm. Find the curved surface area of the
frustum.

Solution 15

Question 16

A solid is composed of a
cylinder with hemispherical ends. If the whole length of the solid is 104 cm
and the radius of each hemispherical end is 7 cm, find the surface area of
the solid.

Solution 16

Question 17

From a solid cylinder
whose height is 15 cm and diameter 16 cm, a conical cavity of the same height
and same “diameter is hollowed out. Find the total surface area of the
remaining solid. (Use
𝜋 = 3.14.)

Solution 17

Question 18

A solid rectangular
block of dimensions 4.4 m, 2.6 in and 1 m is cast into a hollow cylindrical
pipe of internal radius 30 cm and thickness 5 cm. Find the length of the
pipe.

Solution 18

Question 19

An open metal bucket is
in the shape of a frustum of a cone, mounted on a hollow cylindrical base
made of the same metallic sheet. The diameters of the two circular ends of
the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40
cm and that of the cylindrical base is 6 cm. Find the area of the metallic
sheet used to make the bucket. Also, find the volume of water the bucket can
hold, in litres.

Solution 19

Question 20

A fanner connects a pipe
of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m
in diameter and 2 m deep. If the water flows through the pipe at the rate of
4 km/hr, in how much time will the tank be filled completely?

Solution 20

## Chapter 19 – Volume and Surface Areas of Solids Exercise MCQ

Question 1

Choose the correct
answer in each of the following:

A cylindrical pencil sharpened at one
edge is the

combination of

(a) a cylinder and
a cone

(b) a cylinder and
frustum of a cone

(c) a cylinder and
a hemisphere

(d) two cylinders

Solution 1

Correct
option: (a)

A cylindrical pencil sharpened at one
edge is the combination of a cylinder and a cone. Observe the figure, the
lower portion is a cylinder and the upper tapering portion is a cone.

Question 2

A shuttlecock used for playing badminton
is the combination of

(a) cylinder and a
hemisphere

(b) frustum of a
cone and a hemisphere

(c) a cone and a
hemisphere

(d) a cylinder and
a sphere

Solution 2

Correct option: (b)

A shuttlecock used for
playing badminton is the combination of a frustum of a cone and a hemisphere,
the lower portion being the hemisphere and the portion above that being the
frustum of the cone.

Question 3

A funnel is the combination of

(a) a cylinder and
a cone

(b) a cylinder and
a hemisphere

(c) a cylinder and
frustum of a cone

(d) a cone and a
hemisphere

Solution 3

Correct
option: (c)

A funnel is the combination of a cylinder
and frustum of a cone. The lower portion is cylindrical and the upper portion
is a frustum of a cone.

Question 4

A surahi is a
combination of

(a) a sphere and a
cylinder

(b) a hemisphere
and a cylinder

(c) a cylinder and
a cone

(d) two hemispheres
Surahi

Solution 4

Correct
option: (a)

A surahi is a
combination of a sphere and a cylinder, the lower portion is the sphere and
the upper portion is the cylinder.

Question 5

The shape of a glass (tumbler) is usually
in the form of

(a) a cylinder

(b) frustum of a
cone

(c) a cone

(d) a sphere Glass

Solution 5

Correct
option: (b)

The shape of a glass (tumbler)
is usually in the form of a frustum of a cone.

Question 6

The shape of a gill in the gilli-danda game is a combination of

(a) a cone and a
cylinder

(b) two cylinders Gilli

(c) two cones and a
cylinder

(d) two cylinders
and a cone

Solution 6

Correct
option: (c)

The shape of a gill in the gilli-danda game is a combination of two cones and a
cylinder. The cones at either ends with the cylinder in the middle.

Question 7

A plumbline (sahul) is the combination of

(a) a hemisphere
and a cone

(b) a cylinder and
a cone

(c) a cylinder and
frustum of a cone

(d) a cylinder and
a sphere Plumbline

Solution 7

Correct
option: (a)

A plumbline (sahul) is the combination of a hemisphere and a cone, the
hemisphere being on top and the lower portion being the cone.

Question 8

A cone is cut by a plane
parallel to its base and the upper part is removed. The part that is left
over is called

(a) a cone

(b) a sphere

(c) a cylinder

(d) frustum of a
cone

Solution 8

Correct option: (d)

A cone is cut by a plane parallel to its
base and the upper part is removed. The part that is left over is called the
frustum of a cone.

Question 9

During conversion of a solid from one
shape to another, the volume of the new shape will

(a) decrease

(b) increase

(c) remain
unaltered

(d) be doubled

Solution 9

Correct
option: (c)

During conversion of a solid from one
shape to another, the volume of the new shape will remain altered.

Question 10

In a right circular cone, the cross
section made by a plane parallel to the base is a

(a) sphere

(b) hemisphere

(c) circle

(d) a semicircle

Solution 10

Correct option: (c)

In a right circular cone, the cross
section made by a plane parallel to the base is a circle.

Question 11

A solid piece of iron in the form of a cuboid of dimensions (cccm) is moulded to form a solid sphere. The radius of the sphere
is

(a) 19 cm

(b) 21 cm

(c) 23 cm

(d) 25 cm

Solution 11

Question 12

The radius (in cm) of the largest right
circular cone that can be cut out from a cube of edge 4.2 cm is

(a) 2.1

(b) 4.2

(c) 8.4

(d) 1.05

Solution 12

Question 13

A metallic solid sphere of radius 9 cm is
melted to form a solid cylinder of radius 9 cm. The height of the cylinder is

(a) 12 cm

(b) 18 cm

(c) 36 cm

(d) 96 cm

Solution 13

Question 14

A rectangular sheet of paper 40 cm × 22 cm,
is rolled to form a hollow cylinder of height 40 cm. The radius of the
cylinder (in cm) is,

Solution 14

Question 15

The number of solid spheres, each of
diameter 6 cm, that can be made by melting a solid metal cylinder of height
45 cm and diameter 4 cm, is

(a) 2

(b) 4

(c) 5

(d) 6

Solution 15

Question 16

The surface areas of two spheres are in
the ratio 16 : 9. The ratio of their volumes is

(a) 64 : 27

(b) 16:9

(c) 4 :3

(d) 163
: 93

Solution 16

Question 17

If the surface area of a sphere is 616 cm2,
its diameter (in cm) is

(a) 7

(b) 14

(c) 28

(d) 56

Solution 17

Question 18

If the radius of a sphere becomes 3 times
then its volume will become

(a) 3 times

(b) 6 times

(c) 9 times

(d) 27 times

Solution 18

Question 19

If the height of a bucket in the shape of
frustum of a cone is 16 cm and the diameters of its two circular ends are 40
cm and 16 cm then its slant height is

Solution 19

Question 20

A sphere of diameter 18 cm is dropped
into a cylindrical vessel of diameter 36 cm, partly
filled with water. If the sphere is completely submerged then the water level
rises by

(a) 3 cm

(b) 4 cm

(c) 5 cm

(d) 6 cm

Solution 20

Question 21

A solid right circular cone is cut into
two parts at the middle of its height by a plane parallel to its base. The
ratio of the volume of the smaller cone to the whole cone is

(a) 1 : 2

(b) 1 : 4

(c) 1 : 6

(d) 1 : 8

Solution 21

Question 22

The radii of the circular ends of a
bucket of height 40 cm are 24 cm and 15 cm. The slant height (in cm) of the
bucket is

(a) 41

(b) 43

(c) 49

(d) 51

Solution 22

Question 23

A solid is hemispherical at the bottom
and conical (of same radius) above it. If the surface areas of the two parts
are equal then the ratio of its radius and the slant height of the conical
part is

(a) 1 : 2

(b) 2 : 1

(c) 1 : 4

(d) 4 : 1

Solution 23

Question 24

If the radius of the base of a right
circular cylinder is halved, keeping the height the same, then the ratio of
the volume of the cylinder thus obtained to the volume of original cylinder
is

(a) 1 : 2

(b) 2 : 1

(c) 1 : 4

(d) 4: 1

Solution 24

Question 25

A cubical ice-cream brick of edge 22 cm
is to be distributed among some children by filling ice-cream cones of radius
2 cm and height 7 cm up to its brim. How many children will get the ice-cream
cones?

(a) 163

(b) 263

(c) 363

(d) 463

Solution 25

Question 26

(a) 11000

(b) 11100

(c) 11200

(d) 11300

Solution 26

Question 27

Twelve solid spheres of the same size are
made by melting a solid metallic cylinder of base diameter 2 cm and height 16
cm. The diameter of each sphere is

(a) 2 cm

(b) 3 cm

(c) 4 cm

(d) 6 cm

Solution 27

Question 28

The diameters of two circular ends of a
bucket are 44 cm and 24 cm, and the height of the bucket is 35 cm. The
capacity of the bucket is

(a) 31.7 litres

(b) 32.7 litres

(c) 33.7 litres

(d) 34.7 litres

Solution 28

Question 29

The slant height of a bucket is 45 cm and
the radii of its top and bottom are 28 cm and 7 cm respectively. The curved
surface area of the bucket is

(a) 4953 cm2

(b) 4952 cm2

(c) 4951 cm2

(d) 4950 cm2

Solution 29

Question 30

The volumes of two spheres are in the
ratio 64:27. The ratio of their surface area is

(a) 9:16

(b) 16:9

(c) 3:4

(d) 4:3

Solution 30

Question 31

(a) 142296

(b) 142396

(c) 142496

(d) 142596

Solution 31

Question 32

A metallic spherical shell of internal
and external diameters 4 cm and 8 cm respectively, is melted and recast into
the form of a cone of base diameter 8 cm. The height of the cone is

(a) 12 cm

(b) 14 cm

(c) 15 cm

(d) 8 cm

Solution 32

Question 33

A medicine capsule is in the shape of a
cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends.
The length of the entire capsule is 2 cm. The capacity of the capsule is

(a) 0.33 cm3

(b) 0.34 cm3

(c) 0.35 cm3

(d) 0.36 cm3

Solution 33

Question 34

The length of the longest pole that can
be kept in a room (12 m × 9 m × 8 m) is

(a) 29 m

(b) 21 m

(c) 19 m

(d) 17 m

Solution 34

Question 35

Solution 35

Question 36

The
volume of a cube is 2744 cm3. Its surface area is

(a) 196 cm2

(b) 1176 cm2

(c) 784 cm2

(d) 588 cm2

Solution 36

Question 37

The
total surface area of a cube is 864 cm2. Its volume is

(a) 3456 cm3

(b) 432 cm3

(c) 1728 cm3

(d) 3456 cm3

Solution 37

Question 38

How many bricks each measuring (25 cm ×
11.25 cm × 6 cm) will be required to construct a wall (8 m × 6 m × 22.5 cm)?

(a) 8000

(b) 6400

(c) 4800

(d) 7200

Solution 38

Question 39

The area of the base of a rectangular
tank is 6500 cm2 and the volume of water contained in it is 2.6 m3.
The depth of water in the tank is.

(a) 3.5 m

(b) 4 m

(c) 5 m

(d) 8 m

Solution 39

Question 40

The volume of a wall, 5 times as high as
it is broad and 8 times as long as it is high, is 12.8 m3. The

(a) 30 cm

(b) 40 cm

(c) 22.5 cm

(d) 25 cm

Solution 40

Question 41

If the areas of three adjacent faces of a
cuboid are x, y, z respectively then the volume of
the cuboid is

Solution 41

Question 42

(a) 361 cm2

(b) 125 cm2

(c) 236 cm2

(d) 486 cm2

Solution 42

Question 43

If each edge of a cube is increased by
50%, the percentage increase in the surface area is

(a) 50%

(b) 75%

(c) 100%

(d) 125%

Solution 43

Question 44

How many bags of grain can be stored in a
cuboidal granary (8 m× 6m × 3 m), if each bag
occupies a space of 0.64 m3?

(a) 8256

(b) 90

(c) 212

(d) 225

Solution 44

Question 45

A cube of side 6 cm is cut into a number
of cubes each of side 2 cm. The number of cubes formed is

(a) 6

(b) 9

(c) 12

(d) 27

Solution 45

Question 46

In a shower, 5 cm of rain falls. The
volume of the water that falls on 2 hectares of ground, is

(a) 100 m3

(b) 10 m3

(c) 1000 m3

(d) 10000 m3

Solution 46

Question 47

Two cubes have their volumes in the ratio
1: 27. The ratio of their surface areas is

(a) 1 : 3

(b) 1 : 8

(c) 1 : 9

(d) 1 : 18

Solution 47

Question 48

The diameter of the base of a cylinder is
4 cm and its height is 14 cm. The volume of the cylinder is

(a) 176 cm3

(b) 196 cm3

(c) 276 cm3

(d) 352 cm3

Solution 48

Question 49

The diameter of a cylinder is 28 cm and
its height is 20 cm. The total surface area of the cylinder is

(a) 2993 cm2

(b) 2992 cm2

(c) 2292 cm2

(d) 2229 cm2

Solution 49

Question 50

The height of a cylinder is 14 cm and its
curved surface area is 264 cm2. The volume of the cylinder is

(a) 308 cm3

(b) 396 cm3

(c) 1232 cm3

(d) 1848 cm3

Solution 50

Question 51

The curved surface area of a cylinder is
1760 cm2 and its base radius is 14 cm. The height of the cylinder
is

(a) 10 cm

(b) 15 cm

(c) 20 cm

(d) 40 cm

Solution 51

Question 52

The ratio of the total surface area to
the lateral surface area of a cylinder with base radius 80 cm and height 20
cm is

(a) 2 :1

(b) 3:1

(c) 4:1

(d) 5:1

Solution 52

Question 53

The curved surface area of a cylindrical
pillar is 264 m2 and its volume is 924 m3. The height
of the pillar is

(a) 4 m

(b) 5 m

(c) 6 m

(d) 7 m

Solution 53

Question 54

The ratio between the radius of the base
and the height of the cylinder is 2 : 3. If its
volume is 1617 cm3, the total surface area of the cylinder is

(a) 308 cm2

(b) 462 cm2

(c) 540 cm2

(d) 770 cm2

Solution 54

Question 55

The radii of two cylinders are in the
ratio 2:3 and their heights are in the ratio 5 : 3.
The ratio of their volumes is

(a) 27 : 20

(b) 20 : 27

(c) 4 :9

(d) 9 : 4

Solution 55

Question 56

Two circular cylinders of equal volume have
their heights in the ratio 1:2. The ratio of their radii is

Solution 56

Question 57

The radius of the base of a cone is 5 cm
and its height is 12 cm. Its curved surface area is

Solution 57

Question 58

The diameter of the base of a cone is 42
cm and its volume is 12936 cm3. Its height is

(a) 28 cm

(b) 21 cm

(c) 35 cm

(d) 14 cm

Solution 58

Question 59

The area of the base of a right circular
cone is 154 cm2 and its height is 14 cm. Its curved surface area
is

Solution 59

Question 60

On increasing each of the radius of the
base and the height of a cone by 20% its volume will be increased by

(a) 20%

(b) 40%

(c) 60%

(d) 72.8%

Solution 60

Question 61

The radii of the base of a cylinder and a
cone are in the ratio 3:4. If they have their heights in the ratio 2 : 3, the
ratio between their volumes is

(a) 9 :8

(b) 3:4

(c) 8 :9

(d) 4 : 3

Solution 61

Question 62

A metallic cylinder of radius 8 cm and
height 2 cm is melted and converted into a right circular cone of height 6
cm. The radius of the base of this cone is

(a) 4 cm

(b) 5 cm

(c) 6 cm

(d) 8 cm

Solution 62

Question 63

The height of a conical tent is 14 m and
its floor area is 346.5 m2. How much canvas, 1.1 m wide, will be
required for it?

(a) 490 m

(b) 525 m

(c) 665 m

(d) 860 m

Solution 63

Question 64

The
diameter of a sphere is 14 cm. Its volume is

Solution 64

Question 65

The ratio between the volumes of two
spheres is 8: 27. What is the ratio between their surface areas?

(a) 2:3

(b) 4:5

(c) 5:6

(d) 4: 9

Solution 65

Question 66

A hollow metallic sphere with external
diameter 8 cm and internal diameter 4 cm is melted and moulded
into a cone having base radius 8 cm. The height of the cone is

(a) 12 cm

(b) 14 cm

(c) 15 cm

(d) 18 cm

Solution 66

Question 67

A metallic cone having base radius 2.1 cm
and height 8.4 cm is melted and moulded into a
sphere. The radius of the sphere is

(a) 2.1 cm

(b) 1.05 cm

(c) 1.5 cm

(d) 2 cm

Solution 67

Question 68

The volume of a hemisphere is 19404 cm3.
The total surface area of the hemisphere is

(a) 4158 cm2

(b) 16632 cm2

(c) 8316 cm2

(d) 3696 cm2

Solution 68

Correct option: (a)

Question 69

The surface area of a sphere is 154 cm2.
The volume of the sphere is all

Solution 69

Correct option: (a)

Question 70

The
total surface area of a hemisphere of radius 7 cm is

(588
𝜋) cm2

(392
𝜋) cm2

(147
𝜋) cm2

(598
𝜋) cm2

Solution 70

Question 71

The circular ends of a bucket are of
radii 35 cm and 14 cm and the height of the bucket is 40 cm. Its volume is

(a) 60060 cm3

(b) 80080 cm3

(c) 70040 cm3

(d) 80160 cm3

Solution 71

Question 72

If the radii of the ends of a bucket are
5 cm and 15 cm and it is 24 cm high then its surface area is

(a) 1815.3 cm2

(b) 1711.3 cm2

(c) 2025.3 cm2

(d) 2360 cm2

Solution 72

Question 73

A circus tent is cylindrical to a height
of 4 m and conical above it. If its diameter is 105 m and its slant height is
40 m, the total area of canvas required is

(a) 1760 m2

(b) 2640 m2

(c) 3960 m2

(d) 7920 m2

Solution 73

Question 74

Match
the following columns:

 Column I Column II A solid metallic sphere of radius 8 cm is melted and the material is used to make solid right cones with height 4 cm and radius of the base 8 cm. How many cones are formed? (p) 18 A 20-in-deep well with diameter 14 m is dug up and the earth from digging is evenly spread out to form a platform 44 m by 14 in. The height of the platform is …… m. (q) 8 A sphere of radius 6 cm is melted and recast into the shape of a cylinder of radius 4 cm. Then, the height of the cylinder is…… cm. (r) 16 : 9 The volumes of two spheres are in the ratio 64: 27. The ratio of their surface areas is ….. (s) 5

The

(a)-….., (b)- ….. , (c)- ….., (d)- ……

Solution 74

Question 75

Match
the following columns:

 Column I Column II The radii of the circular ends of a bucket in the form of frustum of a cone of height 30 cm are 20 cm and 10 cm respectively. The capacity of the bucket is …….cm3. (p) 2418 π The radii of the circular ends of a conical bucket of height 15 cm are 20 cm and 12 cm respectively. The slant height of the bucket is… cm. (q) 22000 The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. The total surface area of the bucket is …cm2. (r) 12 Three solid metallic spheres of radii 3 cm, 4 cm and 5 cm are melted to form a single solid sphere. The diameter of the resulting sphere is ….cm. (s) 17

(a)-….., (b)-
….. , (c)- ….., (d)- ……

Solution 75

Question 76

Assertional– and-Resons type

Each
question consists of two statements, namely,

Assertion
(A) and Reason (R). For selecting the correct

use the following code:

(a) Both Assertion
(A) and Reason (R) are true and Reason (R) is a correct explanation of
Assertion (A).

(b) Both Assertion
(A) and Reason (R) are true but Reason (R) is not a correct explanation of
Assertion (A).

(c) Assertion (A)
is true and Reason (R) is false.

(d) Assertion (A)
is false and Reason (R) is true.

 Assertion (A) Reason (R) If the radii of the circular ends of a bucket 24 cm high are 15 cm and 5 cm respectively, then the surface area of the bucket is 545π cm2. If the radii of the circular ends of the frustum of a cone are R and r respectively and its height is h, then its surface area is π (R2 + r2 + l(R-r), Where l2 = h2+(R-r)2

/(d) .

Solution 76

Question 77

Assertional– and-Resons type

Each
question consists of two statements, namely,

Assertion
(A) and Reason (R). For selecting the correct

use the following code:

(a) Both Assertion
(A) and Reason (R) are true and Reason (R) is a correct explanation of
Assertion (A).

(b) Both Assertion
(A) and Reason (R) are true but Reason (R) is not a correct explanation of
Assertion (A).

(c) Assertion (A)
is true and Reason (R) is false.

(d) Assertion (A)
is false and Reason (R) is true.

 Assertion (A) Reason (R) A hemisphere of radius 7 cm is to be painted outside on the surface. The total cost of painting at it Rs. 5 per cm2 is Rs. 2300. The total surface area hemisphere is 3πr2.

/(d) .

Solution 77

Question 78

Assertional– and-Resons type

Each
question consists of two statements, namely,

Assertion
(A) and Reason (R). For selecting the correct

use the following code:

(a) Both Assertion
(A) and Reason (R) are true and Reason (R) is a correct explanation of
Assertion (A).

(b) Both Assertion
(A) and Reason (R) are true but Reason (R) is not a correct explanation of
Assertion (A).

(c) Assertion (A)
is true and Reason (R) is false.

(d) Assertion (A)
is false and Reason (R) is true.

 Assertion (A) Reason (R) The number of coins 1.75 cm in diameter and 2 mm thick from a melted cuboid (10 cm× 5.5 cm × 3.5 cm) is 400. Volume of a cylinder of base radius r and height h is given byV = (πr2h) cubic units.And, area of a cuboid= (l × b × h) cubic units.

The
correct answer is (a)/(b)/(c) /(d) .

Solution 78

Question 79

Assertional– and-Resons type

Each
question consists of two statements, namely,

Assertion
(A) and Reason (R). For selecting the correct

use the following code:

(a) Both Assertion
(A) and Reason (R) are true and Reason (R) is a correct explanation of
Assertion (A).

(b) Both Assertion
(A) and Reason (R) are true but Reason (R) is not a correct explanation of
Assertion (A).

(c) Assertion (A)
is true and Reason (R) is false.

(d) Assertion (A)
is false and Reason (R) is true.

 Assertion (A) Reason (R) If the volumes of two spheres are in the ratio 27:8 then their surface areas are in the ratio 3:2.

The
correct answer is (a)/(b)/(c) /(d) .

Solution 79

Question 80

Assertional– and-Resons type

Each
question consists of two statements, namely,

Assertion
(A) and Reason (R). For selecting the correct

use the following code:

(a) Both Assertion
(A) and Reason (R) are true and Reason (R) is a correct explanation of
Assertion (A).

(b) Both Assertion
(A) and Reason (R) are true but Reason (R) is not a correct explanation of
Assertion (A).

(c) Assertion (A)
is true and Reason (R) is false.

(d) Assertion (A)
is false and Reason (R) is true.

 Assertion (A) Reason (R) The curved surface area of a cone of base radius 3 cm and height 4cm is (15π) cm2. Volume of a cone = πr2h.

The
correct answer is (a)/(b)/(c) /(d) .

Solution 80

error: Content is protected !!