R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 15 – Volume and Surface Area of Solids

Chapter 15 – Volume and Surface Area of Solids Exercise Ex. 15A

Question 1

Find the volume, the lateral surface area and the total surface area cuboid whose dimensions are:

Length=12 cm,breadth=8 cm and height =4.5 cm

Solution 1

length =12cm, breadth = 8 cm and height = 4.5 cm

Volume of cuboid = l x b x h

= (12 x 8 x 4.5) cm3= 432 cm3

Lateral surface area of a cuboid = 2(l + b) x h

= [2(12 + 8) x 4.5] cm2

= (2 x 20 x 4.5) cm2 = 180 cm2

Total surface area cuboid = 2(lb +b h+ l h)

= 2(12 x 8 + 8 x 4.5 + 12 x 4.5) cm2

= 2(96 +36 +54) cm2

= (2 x186) cm2

= 372 cm2

Question 2

Find the volume, the lateral surface area and the total surface area cuboid whose dimensions are:

Length =26 m, breadth =14m and height =6.5m

Solution 2

Length 26 m, breadth =14 m and height =6.5 m

Volume of a cuboid= l x b x h

= (26 x 14 x 6.5) m3

= 2366 m3

Lateral surface area of a cuboid =2 (l + b) x h

= [2(26+14) x 6.5] m2

= (2 x 40 x 6.5) m2

= 520 m2

Total surface area= 2(lb+ bh + lh)

= 2(26 x 14+14 x6.5 +26 x6.5)

= 2 (364+91+169) m2

= (2 x 624) m2= 1248 m2.

Question 3

Find the volume, the lateral surface area and the total surface area cuboid whose dimensions are:

Length =15m, breadth =6 m and height =5 dm

Solution 3

Length = 15 m, breadth = 6m and height = 5 dm = 0.5 m

Volume of a cuboid = l x b x h

= (15 x 6 x 0.5) m3=45 m3.

Lateral surface area = 2(l + b) x h

= [2(15 + 6) x 0.5] m2

= (2 x 21×0.5) m2=21 m2

Total surface area =2(lb+ bh + lh)

= 2(15 x 6 +6 x 0.5+ 15 x 0.5) m2

= 2(90+3+7.5) m2

= (2 x 100.5) m2

=201 m2

Question 4

Find the volume, the lateral surface area and the total surface area cuboid whose dimensions are:

Length =24 m, breadth =25 cmand height =6m

Solution 4

Length = 24 m, breadth = 25 cm =0.25 m, height = 6m.

Volume of cuboid= l x b x h

= (24 x 0.25 x 6) m3.

= 36 m3.

Lateral surface area= 2(l + b) x h

= [2(24 +0.25) x 6] m2

= (2 x 24.25 x 6) m2

= 291 m2.

Total surface area =2(lb+ bh + lh)

=2(24 x 0.25+0.25x 6 +24 x 6) m2

= 2(6+1.5+144) m2

= (2 x151.5) m2=303 m2.

Question 5

A wall 15 m long , 30 cm wide and 4 m high is made of bricks, each measuring (22cm x12.5cm x7.5cm) if  of the total volume of the wall consists of mortar , how many bricks are there in the wall ?

Solution 5

L

Question 6

How many cubic centimetres
of iron are there in an open box whose external dimensions are 36 cm, 25 cm,
16.5 cm, the iron being 1.5 cm thick throughout? If
1 cm3 of iron weighs 15 g, find the weight of the empty box in
kilograms.

Solution 6

External
length of the box = 36 cm

External
breadth of the box = 25 cm

External
height of the box = 16.5 cm

External
volume of the box = (36 × 25 × 16.5) cm3
= 14850 cm3

Internal
length of the box = [36 – (1.5
× 2)] cm = 33 cm

Internal
breadth of the box = [25 – (1.5
× 2)] cm = 22 cm

Internal
height of the box = (16.5 – 1.5) cm = 15 cm

Internal
volume of the box = (33 × 22 × 15) cm3
= 10890 cm3

Thus,
volume of iron used in the box

=
External volume of the box – Internal volume of the box

=
(14850 – 10890) cm3

=
3960 cm3

Question 7

A box made of sheet metal costs Rs.6480 at Rs.120 per square metre. If the box
is 5 m long and 3 m wide, find its height.

Solution 7

Question 8

The volume of a cuboid is 1536m3. Its length is 16m, and its breadth and height are in the ratio 3:2. Find the breadth and height of the cuboid.

Solution 8

Question 9

How many persons can be accommodated in a dining hall of dimensions (20m x16mx4.5m), assuring that each person’s requires 5 cubic metres of air?

Solution 9
Question 10

A classroom is 10m long, 6.4 m wide and 5m high. If each student be given 1.6 m2 of the floor area, how many students can be accommodated in the room? How many cubic metres of air would each student get?

Solution 10

Question 11

The surface of the area of a cuboid is 758 cm2. Its length and breadth are 14 cm and 11cm respectively. Find its height.

Solution 11

Question 12
In  shower, 5 cm of rain falls. Find the volume of water that falls on 2 hectares of ground.
Solution 12
Question 13

Find the volume, the lateral surface area, the total surface area and the diagonal of cube, each of whose edges measures 9m. [Take ]

Solution 13

Question 14

The total surface area of a cube is 1176 cm2. Find its volume.

Solution 14

Question 15

A matchbox measures 4 cm ×
2.5 cm ×
1.5 cm. What is the volume of a packet containing 12 such matchboxes?

Solution 15

For
a matchbox,

Length
= 4 cm

= 2.5 cm

Height
= 1.5 cm

Volume
of one matchbox = Volume of cuboid

=
Length

=
(4
× 2.5 × 1.5) cm3

=
15 cm3

Hence,
volume of 12 such matchboxes = 12
× 15 = 180 cm3

Question 16

The lateral surface area of a cube is 900 cm2. Find its volume.

Solution 16

Question 17

The volume of a cube is 512 cm3. Find its surface area.

Solution 17

Question 18

Three cubes of metal with edges 3cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the lateral surface area of the new cube formed.

Solution 18

Question 19

Find the length of the longest pole that can be put in a room of dimensions (10mx 10m x5m).

Solution 19

Question 20

The sum of length, breadth and
depth of a cuboid is 19 cm and length of its diagonal is 11 cm. Find the
surface area of the cuboid.

Solution 20

Question 21

Each edge of a cube is increased
by 50%. Find the percentage increase in the surface area of the cube.

Solution 21

Let
the edge of the cube = ‘a’ cm

Then,
surface area of cube = 6a2 cm2

Question 22

If V is the volume of a cuboid of
dimensions a, b, c and S is its surface area then prove that

Solution 22

Question 23

Water in a canal, 30 dm wide and 12 dm deep, is
flowing with a velocity of 20 km per hour. How much area will it irrigate, if
9 cm of standing water is desired?

Solution 23

Question 24

A solid metallic cuboid of
dimensions (9 m
× 8 m × 2 m) is melted and recast into solid cubes of edge 2 m.
Find the number of cubes so formed.

Solution 24

Volume
of a cuboid = (9
× 8 × 2) m3
= 144 m3

Volume
of each cube of edge 2 m = (2 m)3 = 8 m3

Question 25

A cuboidal water tank is 6 m long,
5 m wide and 4.5 m deep. How many litres of water
can it hold? (Given, 1 m3 = 1000 litres.)

Solution 25

For
a cuboidal water tank,

Length
= 6 m

= 5 m

Height
= 4.5 m

Now,

Volume
of a cuboidal water tank = Length

=
(6
× 5 × 4.5) m3

=
135 m3

=
135
× 1000 litres

=
135000 litres

Thus,
a tank can hold 135000 litres of water.

Question 26

The capacity of a cuboidal tank is
50000 litres of water. Find the breadth of the tank
if its length and depth are respectively 10 m and 2.5 m. (Given, 1000 litres = 1 m3.)

Solution 26

For
a cuboidal water tank,

Length
= 10 m

= 2.5 m

Volume
= 50000 litres = 50 m3

Now,

Volume
of a cuboidal tank = Length

50 = 10 × 2.5 × Height

Height = 2 m =
Depth

Thus,
the depth of a tank is 2 m.

Question 27

A godown
measures 40 m
× 25 m × 15 m. Find the maximum number of wooden crates, each
measuring 1.5 m × 1.25 m × 0.5 m, that can be stored in godown.

Solution 27

For
a godown,

Length
= 40 m

= 25 m

Height
= 15 m

Volume
of a godown = Length

= (40 × 25 × 15) m3

For
each wooden crate,

Length
= 1.5 m

= 1.25 m

Height
= 0.5 m

Volume
of each wooden crate = Length

= (1.5 × 1.25 × 0.5) m3

Question 28

How many planks of dimensions (5mx25cmX10cm) can be stored in a pit which is 20 m long , 6 m wide and 80 cm deep ?

Solution 28

Question 29

How many bricks will be required to construct a wall 8 m long , 6 m high and 22.5 cm thick if each brick measures (25cm x11.25cm x 6cm)?

Solution 29

Question 30

Find the capacity of a closed rectangular cistern whose length is 8 m, breadth 6 m and depth 2.5 m. Also, find the area of the iron sheet required to make the cistern.

Solution 30

Length of Cistern = 8 m

Breadth of Cistern = 6 m

And Height (depth) of Cistern =2.5 m

Capacity of the Cistern = Volume of cistern

Volume of Cistern = (l x b x h)

= (8 x 6 x2.5) m3

=120 m3

Area of the iron sheet required = Total surface area of the cistem.

Total surface area = 2(lb +bh +lh)

= 2(8 x 6 + 6×2.5+ 2.5×8) m2

= 2(48 + 15 + 20) m2

= (2 x 83) m2=166 m2

Question 31

The dimensions of a room are (9 m ×
8 m ×
6.5 m). It has one door of dimensions (2 m ×
1.5 m) and two windows, each of dimensions (1.5 m ×
1 m). Find the cost of whitewashing the walls at Rs.25 per square metre.

Solution 31

Area
of four walls of the room = 2(length + breadth)
× Height

=
[2(9 + 8)
× 6.5] m2

=
(34
× 6.5) m2

=
221 m2

Area
of one door = Length × Breadth = (2
× 1.5) m2 = 3 m2

Area
of two windows = 2

=
[2
× (1.5 × 1)] m2

=
(2
× 1.5) m2

=
3 m2

Area
to be whitewashed

=
Area of four walls of the room – Area of one door – Area of two windows

=
(221 – 3 – 3) m2

=
215 m2

Cost
of whitewashing = Rs. 25 per square metre

Cost of
whitewashing 215 m2 = Rs. (25 × 215) = Rs. 5375

Chapter 15 – Volume and Surface Area of Solids Exercise Ex. 15B

Question 1

The diameter of a cylinder is 28 cm and its height is 40 cm. find the curved surface area, total surface area and the volume of the cylinder.

Solution 1

Question 2

In a water heating system, there
is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total

Solution 2

Diameter of a
cylindrical pipe = 5 cm

cylindrical pipe = 2.5 cm

Height (h) of a
cylindrical pipe = 28 m = 2800 cm

Question 3

Find the weight of a solid cylinder of radius10.5 cm and height 60 cm if the material of the cylinder weights 5 g per cm2

Solution 3
Question 4

The curved surface area of a cylinder is 1210 cm2 and its diameter is 20 cm. find its height and volume.

Solution 4

Question 5

The curved surface area of a cylinder is 4400 cm2 and the circumferences of its base are 110 cm. Find the height and the volume of the cylinder.

Solution 5
Question 6

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

Solution 6

Question 7

The total surface area of the cylinder is 462 cm2. And its curved surface area is one third of its total surface area. Find the volume of the cylinder.

Solution 7

Question 8

The total surface area of the solid cylinder is 231 cm2 and its curved surface area is of the total surface area. Find the volume of the cylinder.

Solution 8

Question 9

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1:2. Find the volume of the cylinder if its total surface area is 616 cm2.

Solution 9

Question 10

A cylindrical bucket , 28 cm in diameter and 72 cm high , is full of water .The water is emptied into a rectangular tank, 66 cm long and 28 cm wide. Find the height of the water level in the tank

Solution 10

Question 11

The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up on writing 330 words on an average. How many words would use up a bottle of ink containing one fifth of a liter?

Solution 11

Question 12

A patient in a hospital is given
soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with
soup to a height of 4 cm, how much soup the hospital has to prepare daily to
serve 250 patients?

Solution 12

cylindrical bowl =

Height (h) up to which
the bowl is filled with soup = 4 cm

Volume of soup in 1 bowl
=
pr2h  = 154 cm3

Hence, volume of soup in
250 bowls = (250
× 154) cm3 = 38500 cm3
= 38.5 litres

Thus, the hospital will
have to prepare 38.5 litres of soup daily to serve
250 patients.

Question 13

1 cm3 of gold is drawn into a wire 0.1 mm is diameter. Find the length of a wire.

Solution 13

Question 14

Ifs 1 cm3 of cast iron weighs 21 g, find the weight of a cast iron pipe of length 1 m with a bore of 3 cm in which the thickness of the metal is 1 cm.

Solution 14

Question 15

A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal.

Solution 15

Question 16

It is required to make a closed
cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet.
How many square metres of the sheet are required
for the same?

Solution 16

Diameter of a cylinder =
140 cm

cm

Height (h) of a cylinder
= 1 m = 100 cm

Question 17

A juiceseller
has a large cylindrical vessel of base radius 15 cm filled up to a height of
32 cm with orange juice. The juice is filled in small cylindrical glasses of
radius 3 cm up to a height of 8 cm, and sold for
Rs.15 each, How much money does he receive by selling the
juice completely?

Solution 17

vessel = 15 cm

Height (h) of
cylindrical vessel = 32 m

cylindrical glass = 3 cm

Height of a small
cylindrical glass = 8 cm

Question 18

A well with inside diameter 10 m
is dug 8.4 m deep. Earth taken out of it is spread all around it to a width
of 7.5 m to form an embankment. Find the height of the embankment.

Solution 18

of the well = 5 m

Depth
of the well = 8.4 m

Width
of the embankment = 7.5 m

External
radius of the embankment, R = (5 + 7.5) m = 12.5 m

Internal
radius of the embankment, r = 5 m

Area
of the embankment = π (R2 – r2)

Volume
of the embankment = Volume of the earth dug out = 660 m2

Question 19

How many litres
of water flows out of a pipe having an area of cross section of 5 cm2
in 1 minute, if the speed of water in the pipe is 30 cm/sec?

Solution 19

Speed
of water = 30 cm/sec

Volume of
water that flows out of the pipe in one second

=
Area of cross-section
× Length of water flown in one
second

=
(5
× 30) cm3

=
150 cm3

Hence,
volume of water that flows out of the pipe in 1 minute

=
(150
× 60) cm3

=
9000 cm3

=
9 litres

Question 20

A cylindrical water tank of
diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm
through which water flows at the rate of 2 m per second. In how much time
will the tank be filled?

Solution 20

Suppose
the tank is filled in x minutes. Then,

Volume
of the water that flows out through the pipe in x minutes

=
Volume of the tank

Hence,
the tank will be filled in 28 minutes.

Question 21

A cylindrical container with
diameter of base 56 cm contains sufficient water to submerge a rectangular
solid of iron with dimensions (32 cm
× 22 cm × 14 cm). Find the rise in the level of water when the
solid is completely submerged.

Solution 21

Let
the rise in the level of water = h cm

Then,

Volume
of the cylinder of height h and base radius 28 cm

=
Volume of rectangular iron solid

Thus,
the rise in the level of water is 4 cm.

Question 22

Find the cost of sinking a
tube-well 280 m deep, having a diameter 3 m at the rate of
Rs.15 per cubic metre. Find also
the cost of cementing its inner curved surface at Rs.10 per square metre.

Solution 22

r = 1.5 m

Height,
h = 280 m

Question 23

The pillars of a temple are
cylindrically shaped. Each pillar has a circular base of radius 20 cm and
height 10 m. How much concrete mixture would be required to build 14 such
pillars?

Solution 23

20 cm =  m

Height (h) of pillar = 10
m

Question 24

Find the length of 13.2 kg of
copper wire of diameter 4 mm, when 1 cubic centimetre
of copper weights 8.4 g.

Solution 24

Let
the length of the wire = ‘h’ metres

Then,

Volume
of the wire × 8.4 g = (13.2 × 1000) g

Thus,
the length of the wire is 125 m.

Question 25

It costs Rs.3300 to paint the inner curved surface of a cylindrical
vessel 10 m deep at the rate of Rs.30 per m2. Find the

(i) inner curved surface area of the vessel,

(ii) inner radius of the base, and

(iii) capacity of the vessel.

Solution 25

Question 26

The difference between inside and
outside surfaces of a cylindrical tube 14 cm long, is 88 cm2. If
the volume of the tube is 176 cm3, find the inner and outer radii
of the tube.

Solution 26

Let
R cm and r cm be the outer and inner radii of the cylindrical tube.

We
have, length of tube = h = 14 cm

Now,

Outside
surface area – Inner surface area = 88 cm2

2πRh – 2πrh = 88

2π(R – r)h =
88

It
is given that the volume of the tube = 176 cm3

External
volume – Internal volume = 176 cm3

πR2h
– πr2h = 176

π (R2
– r2)h = 176

(i) and (ii), we get

2R
= 5

R = 2.5 cm

2.5 – r = 1

r = 1.5 cm

Thus,
the inner and outer radii of the tube are 1.5 cm and 2.5 cm respectively.

Question 27

A rectangular sheet of paper 30 cm
×
18 cm can be transformed into the curved surface of a right circular cylinder
in two ways namely, either by rolling the paper along its length or by
rolling it along its breadth. Find the ratio of the volumes of the two
cylinders, thus formed.

Solution 27

When
the sheet is folded along its length, it forms a cylinder of height, h1
= 18 cm and perimeter of base equal to 30 cm.

Let
r1 be the radius of the base and V1 be is volume.

Then,

Again,
when the sheet is folded along its breadth, it forms a cylinder of height, h2
= 30 cm and perimeter of base equal to 18 cm.

Let
r2 be the radius of the base and V2 be is volume.

Then,

Question 28

A soft drink is available in two
packs: (i) a tin can with a rectangular base of
length 5 cm, breadth 4 cm and height 15 cm, and (ii) a plastic cylinder with
circular base of diameter 7 cm and height 10 cm. Which container has greater
capacity and by how much?

Solution 28

For
a tin can of rectangular base,

Length
= 5 cm

= 4 cm

Height
= 15 cm

Volume of a
tin can = Length × Breadth × Height

=
(5
× 4 × 15) cm3

=
300 cm3

For
a cylinder with circular base,

Diameter
= 7
⇒ Radius = r = cm

Height
= h = 10 cm

Volume of
plastic cylinder is greater than volume of a tin can.

Difference
in volume = (385 – 300) = 85 cm3

Thus,
a plastic cylinder has more capacity that a tin can by 85 cm3.

Question 29

There are 20 cylindrical pillars
in a building, each having a diameter of 50 cm and height 4 m. Find the cost
of cleaning them at
Rs.14 per m2.

Solution 29

Radius (r) of 1 pillar =

Height (h) of 1 pillar =
4 m

Question 30

The curved surface area of a right
circular cylinder is 4.4 m2. If the radius of its base is 0.7 m,
find its (i) height and (ii) volume.

Solution 30

Curved surface area of a
cylinder = 4.4 m2

= 0.7 m

Question 31

The lateral surface area of a
cylinder is 94.2 cm2 and its height is 5 cm. Find (i) the radius of its base and (ii) its volume. (Take π =
3.14.)

Solution 31

Lateral surface area of
a cylinder = 94.2 cm2

Height (h) of a cylinder
= 5 cm

Question 32

The capacity of a closed
cylindrical vessel of height 1 m is 15.4 litres.
Find the area of the metal sheet needed to make it.

Solution 32

Volume of a cylinder =
15.4 litres = 15400 cm3

Height (h) of a cylinder
= 1 m = 100 cm

Question 33

The inner diameter of a
cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length
of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood
has a mass of 0.6 g.

Solution 33

Internal
diameter of a cylinder = 24 cm

Internal
radius of a cylinder, r = 12 cm

External
diameter of a cylinder = 28 cm

External
radius of a cylinder, R = 14 cm

Length
of the pipe, i.e height, h = 35 cm

Chapter 15 – Volume and Surface Area of Solids Exercise Ex. 15C

Question 1

Find the curved surface area of a
cone with base radius 5.25 cm and slant height 10 cm.

Solution 1

of a cone, r = 5.25 cm

Slant
height of a cone, l = 10 cm

Question 2

A conical pit of diameter 3.5 m is
12 m deep. What is its capacity in kilolitres?

HINT 1 m3 = 1 kilolitre.

Solution 2

Question 3

A heap of wheat is in the form of
a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas
cloth is required to just cover the heap? (Use π = 3.14.)

Solution 3

of a conical heap, r = 4.5 m

Height
of a conical tent, h = 3.5 m

Question 4

A man uses a piece of canvas
having an area of 551 m2, to make a conical tent of base radius 7
m. Assuming that all the stitching margins and wastage incurred while
cutting, amount to approximately 1 m2, find the volume of the tent
that can be made with it.

Solution 4

of a conical tent, r = 7 m

Area
of canvas used in making conical tent = (551 – 1) m2 = 550 m2

Curved surface
area of a conical tent = 550 m2

Question 5

How many meters of cloth , 2.5 m wide , will be required to make conical tent whose base radius is 7 m and height 24 metres?

Solution 5

Question 6

Two cones have their height in the ratio 1:3 and the radii of their bases in the ratio3: 1. Show that their volumes are in the ratio 3:1.

Solution 6

Question 7

A cylinder and a cone have equal radii of their bases and equal height s. If their curved surface areas are in the ratio 8:5, show that the radius and height of each has the ratio 3:4.

Solution 7

Question 8

A right circular cone is 3.6 cm height and the radius of its base is 1.6 cm. It is melted and recast into a right circular cone having base radius 1.2 cm. Find its height.

Solution 8

Question 9

A circus tent is cylindrical to a height of 3 meters and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent.

Solution 9

Question 10

An iron pillarconsistsof a cylindricalportion2.8 m highand 20cm indiameterand a cone42 cm high is surmounting it . Find the weight of the pillar, given that 1 cm3 of iron weights 7.5 g.

Solution 10

Question 11

From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and the base is removed .find the volume of the remaining solid. (Take =3.14)

Solution 11

Question 12

Find the total surface area of a
cone, if its slant height is 21 m and diameter of its base is 24 m.

Solution 12

of a cone, r = 12 m

Slant
height of a cone, l = 21 cm

Question 13

Water flows at the rate of 10 meters per minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the surface 40 cm and depth 24 cm?

Solution 13

Question 14

A cloth having an area of 165 m2
is shaped into the form of a conical tent of radius 5 m. (i) How many
students can sit in the tent if a student, on an average, occupies m2 on the ground? (ii) Find the volume of the
cone.

Solution 14

Curved
surface area of the tent = Area of the cloth = 165 m2

Question 15

A joker’s cap is in the form of a
right circular cone of base radius 7 cm and height 24 cm. Find the area of
the sheet required to make 10 such caps.

Solution 15

of a conical cap, r = 7 cm

Height
of a conical cap, h = 24 cm

Thus, 5500 cm2
sheet will be required to make 10 caps.

Question 16

The curved surface area of a cone
is 308 cm2 and its slant height is 14 cm. Find the radius of the
base and total surface area of the cone.

Solution 16

Let
r be the radius of a cone.

Slant
height of a cone, l = 14 cm

Curved
surface area of a cone = 308 cm2

Question 17

The slant height and base diameter
of a conical tomb are 25 m and 14 m respectively. Find the cost of
whitewashing its curved surface at the rate of
Rs.12 per m2.

Solution 17

of a cone, r = 7 m

Slant
height of a cone, l = 25 m

Cost
of whitewashing = Rs. 12 per m2

Cost of
whitewashing 550 m2 area = Rs. (12 ×
550) = Rs. 6600

Question 18

A conical tent is 10 m high and
radius of its base is 24 m. Find the slant height of the tent. If the cost of
1 m2 canvas is
Rs.70, find the cost of canvas required to make the tent.

Solution 18

of a conical tent, r = 24 m

Height
of a conical tent, h = 10 m

Question 19

A bus stop is barricaded from the
remaining part of the road by using 50 hollow cones made of recycled
cardboard. Each one has a base diameter of 40 cm and height 1 m. If the outer
side of each of the cones is to be painted and the cost of painting is
Rs.25 per m2, what will be the cost of painting
all these cones? (Use π = 3.14 and 1.02.)

Solution 19

Question 20

Find the volume, curved surface
area and the total surface area of a cone having base radius 35 cm and height
12 cm.

Solution 20

Question 21

Find the volume, curved surface area and the total surface area of a cone whose height and slant heights are 6 cm and 10 cm respectively. (Take =3.14)

Solution 21

Chapter 15 – Volume and Surface Area of Solids Exercise Ex. 15D

Question 1

Find the volume and the surface area of a sphere whose radius is

3.5 cm

Solution 1

Question 2

Find the volume and the surface area of a sphere whose radius is

4.2 cm

Solution 2

Question 3

Find the volume and the surface area of a sphere whose radius is:

5 m

Solution 3

Question 4

How many spheres 12 cm in diameter can be made from a metallic cylinder of diameter 8 cm and

height 90 cm ?

Solution 4

Question 5

The diameter of sphere is 6 cm. It is melted and drawn into wire of diameter 2 mm. Find the length of the wire.

Solution 5

Question 6

The diameter of the copper sphere is 18cm. 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 6

Question 7

A sphere of a diameter 15.6 cm is melted and cast into a right circular cone of height 31.2 cm. find the diameter of the base of the cone.

Solution 7

Question 8

A spherical cannonball 28 cm in diameter is melted and recast into a right circular cone mould,  whose base is 35 cm in diameter. Find the height of the cone.

Solution 8

Question 9

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

Solution 9

Question 10

The radii of two spheres are in the ratio 1:2. Find the ratio of their surface areas.

Solution 10

Question 11

The surface areas of two spheres are in the ratio 1:4. Find the ratio of their volumes.

Solution 11

Question 12

A cylindrical tub of a radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75cm.what is the radius of the ball?

Solution 12

Question 13

A cylindrical bucket with base radius 15 cm is filled with water to up height of 20 cm. a heavy iron spherical ball of radius 9 cm is dropped into the bucket to submerge completely in the water . Find the increase in the level of water

Solution 13

Question 14

The volume of a sphere is 38808 cm3. Find the radius and hence its surface area.

Solution 14

Question 15

The outer diameter of a spherical shell is 12 cm and its inner diameter is 8 cm. Find the volume of metal contained in the shell. Also, find its outer surface area.

Solution 15

Question 16

A hollow spherical shell is made of a metal of density 4.5 g per cm3. If it’s internal and external radii are 8 cm and 9cm respectively, find the weight of the shell.

Solution 16

Question 17

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

Solution 17

Question 18

A hemisphere bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped bottles of diameter 3 cm and height 4 cm. How many bottles are required to empty the bowl?

Solution 18

Question 19

A hemispherical bowl is made of steel 0.5 cm thick. The inside radius of the bowl is 4 cm. Find the volume of steel used in making the bowl.

Solution 19

Question 20

A hemispherical bowl is made of
steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer
curved surface area of the bowl.

Solution 20

Inner

Outer radius = 5 + 0.25 = 5.25 cm

Question 21

A hemispherical bowl made of brass
has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at
the rate of
Rs.32
per 100 cm2.

Solution 21

Inner
diameter of the hemispherical bowl = 10.5 cm

Question 22

The diameter of the moon is
approximately one fourth of the diameter of the earth. What fraction of the
volume of the earth is the volume of the moon?

Solution 22

Let the diameter of
earth = d

=

Then, diameter of moon = .

=

Volume of moon

Volume of earth

Thus, the volume of moon
is of volume of earth.

Question 23

Volume and surface area of a solid
hemisphere are numerically equal. What is the diameter of the hemisphere?

Solution 23

Volume
of a solid hemisphere = Surface area of a solid hemisphere

Question 24

Find the surface area of a sphere whose volume is 606.375 m3

Solution 24

Question 25

Find the volume of a sphere whose
surface area is 154 cm2.

Solution 25

Surface
area of sphere = 154 cm2

4πr2
= 154

Question 26

The surface area of a sphere is (576) cm2. Find its volume.

Solution 26

Question 27

How many leads shots, each 3 mm in diameter, can be made from cuboid with dimensions  (12cm x 11cm x 9cm)?

Solution 27

Question 28

Solution 28

Question 29

A solid sphere of radius 3 cm is melted and then cast into smaller spherical balls, each of diameters 0.6 cm. find the number of small balls thus obtained.

Solution 29

Question 30

A metallic sphere of radius 10.5 cm is melted an then recast into smaller cones , each of radius 3.5 cm and height 3 cm. How many cones are obtained?

Solution 30

Chapter 15 – Volume and Surface Area of Solids Exercise MCQ

Question 1

height of a cuboid are 15 cm, 12 cm and 4.5 cm respectively. Its volume is

1. 243
cm3
2. 405
cm3
3. 810
cm3
4. 603
cm3
Solution 1

Question 2

How many persons can be
accommodated in a dining hall of dimensions (20 m
× 15 m × 4.5 m),
assuming that each person requires 5 m3 of air?

1. 250
2. 270
3. 320
4. 300
Solution 2

Question 3

A river 1.5 m deep and
30 m wide is flowing at the rate of 3 km per hour. The volume of water that
runs into the sea per minute is

1. 2000
m3
2. 2250
m3
3. 2500
m3
4. 2750
m3
Solution 3

Question 4

The lateral surface area
of a cube is 256 m2. The volume of the cube is

1. 64
m3
2. 216
m3
3. 256
m3
4. 512
m3
Solution 4

Question 5

The total surface area
of a cube is 96m2. The volume of the cube is

1. 8
cm3
2. 27cm3
3. 64cm3
4. 512
cm3
Solution 5

Question 6

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

1. 256
cm2
2. 384
cm2
3. 512
cm2
4. 64
cm2
Solution 6

Question 7

The length of the
longest rod that can fit in a cubical vessel of side 10 cm is

1. 10
cm
2. 20
cm
3.
Solution 7

Question 8

If the length of
diagonal of a cube is  cm, then its surface
area is

1. 192
cm2
2. 384
cm2
3. 512
cm2
4. 768
cm2
Solution 8

Question 9

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

1. 50%
2. 75%
3. 100%
4. 125%
Solution 9

Question 10

Three cubes of metal
with edges 3 cm, 4 cm and 5 cm respectively are melted to form a single cube.
The lateral surface area of the new cube formed is

1. 72
cm2
2. 144
cm2
3. 128
cm2
4. 256
cm2
Solution 10

Question 11

In a shower, 5 cm of
rain falls, what is the volume of water that falls on 2 hectors of ground?

1. 500
m3
2. 750
m3
3. 800
m3
4. 1000
m3
Solution 11

Question 12

A cuboid is 12 cm long,
9 cm broad and 8 cm high. Its total surface area is

1. 864
cm2
2. 552
cm2
3. 432
cm2
4. 276
cm2
Solution 12

Question 13

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

1. 1:3
2. 1:8
3. 1:9
4. 1:18
Solution 13

Question 14

If each side of a cube
is doubled, then its volume

1. is
doubled
2. becomes
4 times
3. becomes
6 times
4. becomes
8 times
Solution 14

Question 15

The
diameter of a base of a cylinder is 6 cm and its height is 14 cm. The volume
of the cylinder is

a. 198 cm3

b. 396 cm3

c. 495 cm3

d. 297 cm3

Solution 15

Question 16

The diameter of a
cylinder is 28 cm and its height is 20 cm, then its curved surface area is

1. 880
cm2
2. 1760
cm2
3. 3520
cm2
4. 2640
cm2
Solution 16

Question 17

If the curved surface
area of a cylinder is 1760 cm2 and its base radius is 14 cm, then
its height is

1. 10
cm
2. 15
cm
3. 20
cm
4. 40
cm
Solution 17

Question 18

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

1. 308 cm2
2. 396 cm2
3. 1232 cm2
4. 1848 cm2
Solution 18

Question 19

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

1. 4
m
2. 5
m
3. 6
m
4. 7
m
Solution 19

Question 20

cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. The
ratio of their surface area is

1. 2:5
2. 8:7
3. 10:9
4. 16:9
Solution 20

Question 21

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

1. 27:20
2. 20:27
3. 4:9
4. 9:4
Solution 21

Question 22

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

1. 308
cm2
2. 462
cm2
3. 540
cm2
4. 770
cm2
Solution 22

Question 23

height of a cuboid are 15m, 6m, and 5 dm respectively. The lateral surface
area of the cuboid is

1. 45
m2
2. 21
m2
3. 201
m2
4. 90
m2
Solution 23

Question 24

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

Solution 24

Question 25

The ratio between the
curved surface area and the total surface area of a right circular cylinder
is 1:2. If the total surface area is 616 cm2, then the volume of
the cylinder is

1. 1078
cm3
2. 1232
cm3
3. 1848
cm3
4. 924
cm3
Solution 25

Question 26

In a cylinder, if the
radius is halved and the height is doubled, then the volume will be

1. The
same
2. Doubled
3. Halved
4. Four
times
Solution 26

Question 27

The number of coins 1.5
cm in diameter and 0.2 cm thick to be melted to form a right circular
cylinder of height 10 cm and diameter 4.5 cm is

1. 540
2. 450
3. 380
4. 472
Solution 27

Question 28

The radius of a wire is
decreased to one-third. If volume remains the same, the length will become

1. 2
times
2. 3
times
3. 6
times
4. 9
times
Solution 28

Question 29

The diameter of a
roller, 1m long is 84 cm. If it takes 500 complete revolutions to level a
playground, the area of the playground is

1. 1440
m2
2. 1320
m2
3. 1260
m2
4. 1550
m2
Solution 29

Question 30

2.2 dm3 of
lead is to be drawn into a cylindrical wire 0.50 cm in diameter. The length
of the wire is

1. 110
m
2. 112
m
3. 98
m
4. 124
m
Solution 30

Question 31

The lateral surface area
of a cylindrical is

Solution 31

Question 32

The height of a cone is
24 cm and the diameter of its base is 14 cm. The curved surface area of the
cone is

1. 528
cm2
2. 550
cm2
3. 616
cm2
4. 704
cm2
Solution 32

Question 33

The volume of a right
circular cone of height is 12 cm and base radius 6 cm, is

1. (12π) cm3
2. (36π) cm3
3. (72π) cm3
4. (144π) cm3
Solution 33

Question 34

A beam 9 m long, 40 cm
wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is

1. 27
kg
2. 48
kg
3. 36
kg
4. 56
kg
Solution 34

Question 35

How much cloth 2.5 m
wide will be required to make a conical tent having base radius 7 m and
height 24 m?

1. 120
m
2. 180
m
3. 220
m
4. 550
m
Solution 35

Question 36

The volume of a cone is
1570 cm3 and its height is 15 cm. What is the radius of the cone?
(Use
π = 3.14)

1. 10
cm
2. 9
cm
3. 12
cm
4. 8.5
cm
Solution 36

Question 37

The height of cone is 21 cm and its slant height is 28 cm. The volume of the cone is

1. 7356 cm3
2. 7546 cm3
3. 7506 cm3
4. 7564 cm3
Solution 37

Correct option: (b)

Question 38

The volume of a right
circular cone of height 24 cm is 1232 cm3. Its curved surface area
is

1. 1254
cm2
2. 704
cm2
3. 550
cm2
4. 462
cm2
Solution 38

Question 39

If the volumes of two
cones be in the ratio 1:4 and the radii of their bases be in the ratio 4:5,
then the ratio of their heights is

1. 1:5
2. 5:4
3. 25:16
4. 25:64
Solution 39

Question 40

If the height of a cone
is doubled, then its volume is increased by

1. 100%
2. 200
%
3. 300
%
4. 400
%
Solution 40

Question 41

The curved surface area
of the cone is twice that of the other while the slant height of the latter
is twice that of the former. The ratio of their radii is

1. 2:1
2. 4:1
3. 8:1
4. 1:1
Solution 41

Question 42

The ratio of the volumes
of a right circular cylinder and a right circular cone of the same base and
same height will be

1. 1:3
2. 3:1
3. 4:3
4. 3:4
Solution 42

Question 43

A right circular
cylinder and a right circular cone have the same radius and the same volume.
The ratio of the height of the cylinder to that of the cone is

1. 3:5
2. 2:5
3. 3:1
4. 1:3
Solution 43

Question 44

of a cylinder and a cone are in the ratio 3:4 and their heights are in the
ratio 2:3. Then their volumes are in the ratio

1. 9:8
2. 8:9
3. 3:4
4. 4:3
Solution 44

Question 45

The length of the
longest rod that can be placed in a room of dimensions (10 m
× 10 m × 5 m) is

1. 15
m
2. 16
m
3.
4. 12
m
Solution 45

Question 46

If the height and the radius of cone are
doubled, the volume of the cone becomes

1. 3
times
2. 4
times
3. 6
times
4. 8
times
Solution 46

Question 47

A solid metallic cylinder of base radius
3 cm and height 5 cm is melted to make n solid cones of height 1 cm and base
radius 1 mm. The value of n is

1. 450
2. 1350
3. 4500
4. 13500
Solution 47

Question 48

A conical tent is to accommodate 11
persons such that each person occupies 4 m2 of space on the
ground. They have 220m3 of air to breathe. The height of the cone
is

1. 14m
2. 15
m
3. 16
m
4. 20
m
Solution 48

Question 49

The volume of a sphere of radius 2r is

Solution 49

Question 50

The volume of a sphere of a radius 10.5
cm is

1. 9702
cm3
2. 4851
cm3
3. 19404
cm3
4. 14553
cm3
Solution 50

Question 51

The surface area of a sphere of radius 21
cm is

1. 2772
cm2
2. 1386
cm2
3. 4158
cm2
4. 5544
cm2
Solution 51

Question 52

The surface area of a sphere is 1386 cm2.
Its volume is

1. 1617
cm3
2. 3234
cm3
3. 4851
cm3
4. 9702
cm3
Solution 52

Question 53

If the surface area of a sphere is (144 π) m2,
then its volume is

1. (288
π) m3
2. (188
π) m3
3. (300
π) m3
4. (316
π) m3
Solution 53

Question 54

The volume of a sphere is 38808 cm3.
Its curved surface area is

1. 5544
cm2
2. 8316
cm2
3. 4158
cm2
4. 1386
cm2
Solution 54

Question 55

If the ratio of the volumes of two
spheres is 1:8, then the ratio of their surface area is

1. 1:2
2. 1:4
3. 1:8
4. 1:16
Solution 55

Question 56

What is the maximum
length of a pencil that can be placed in a rectangular box of dimensions (8
cm
× 6 cm × 5 cm)?

1. 8
cm
2. 9.5
cm
3. 19
cm
4. 11.2
cm
Solution 56

Question 57

A solid metal ball of radius 8 cm is
melted and cast into smaller balls, each of radius 2 cm, The number of such
balls is

1. 8
2. 16
3. 32
4. 64
Solution 57

Question 58

A cone is 8.4 cm high and the radius of
its base is 2.1 cm. It is melted and recast into a sphere. The radius of the
sphere is

1. 4.2
cm
2. 2.1
cm
3. 2.4
cm
4. 1.6
cm
Solution 58

Question 59

melted and then drawn into a wire of diameter 0.2 cm. The length of wire is

1. 272
m
2. 288
m
3. 292
m
4. 296
m
Solution 59

Question 60

A metallic sphere of radius 10.5 cm is
melted and then recast into small cones, each of radius 3.5 cm and height 3
cm. The number of such cones will be

1. 21
2. 63
3. 126
4. 130
Solution 60

Question 61

How many lead shots, each 0.3 cm in
diameter, can be made from a cuboid of dimensions 9 cm × 11 cm × 12 cm?

1. 7200
2. 8400
3. 72000
4. 84000
Solution 61

Question 62

The diameter of a sphere is 6 cm. It is
melted and drawn into a wire of diameter 2 mm. The length of the wire is

1. 12
m
2. 18
m
3. 36
m
4. 66
m
Solution 62

Question 63

A sphere of diameter 12.6 cm is melted
and cast into a right circular cone of height 25.2 cm. The radius of the base
of the cone is

1. 6.3
cm
2. 2.1
cm
3. 6
cm
4. 4
cm
Solution 63

Question 64

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

1. 1
cm
2. 1.5
cm
3. 2.5
cm
4. 0.5
cm
Solution 64

Question 65

The radius of a hemispherical balloon increases
from 6 cm to 12 cm as air is being pumped into it. The ratio of the surface
areas of the balloons in two cases is

1. 1:4
2. 1:3
3. 2:3
4. 1:2
Solution 65

Question 66

The volumes of the two
spheres are in the ratio 64:27 and the sum of their radii is 7 cm. The
difference of their total surface areas is

1. 38
cm2
2. 58
cm2
3. 78
cm2
4. 88
cm2
Solution 66

Question 67

The number of planks of
dimensions (4 m
× 5 m × 2 m) that can
be stored in a pit which is 40 m long, 12 m wide and 16 m deep is

1. 190
2. 192
3. 184
4. 180
Solution 67

Question 68

A hemispherical bowl of
radius 9 cm contains a liquid. This liquid is to be filled into cylindrical
small bottles of diameter 3 cm and height 4 cm. How many bottles will be
needed to empty the bowl?

1. 27
2. 35
3. 54
4. 63
Solution 68

Question 69

A cone and a hemisphere
have equal bases and equal volumes. The ratio of their heights is

1. 1:2
2. 2:1
3. 4:1
Solution 69

Question 70

A cone, a hemisphere and
a cylinder stand on equal bases and have the same height. The ratio of their
volumes is

1. 1:2:3
2. 2:1:3
3. 2:3:1
4. 3:2:1
Solution 70

Question 71

If the volumes and the
surface area of sphere are numerically the same, then its radius is

1. 1
units
2. 2 units
3. 3
units
4. 4
units
Solution 71

Question 72

How many planks of
dimensions (5 m
× 25 cm × 10 cm) can be
stored in a pit which is 20 m long, 6 m wide and 50 cm deep?

1. 480
2. 450
3. 320
4. 360
Solution 72

Question 73

How many bricks will be
required to construct a wall 8 m long, 6 m high and 22.5 cm thick if each
brick measures (25 cm
× 11.25 cm × 6 cm)?

1. 4800
2. 5600
3. 6400
4. 5200
Solution 73

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