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Question 1:

Find the volume, lateral surface area and the total surface area of the cuboid whose dimensions are:
(i) length = 22 cm, breadth = 12 cm and height = 7.5 cm
(ii) length = 15 m, breadth = 6 m and height = 9 dm
(iii) length = 24 m, breadth = 25 cm and height = 6 m
(iv) length = 48 cm, breadth = 6 dm and height = 1 m

Volume of a cuboid $=\left(Length×Breadth×Height\right)$ cubic units
Total surface area $=2\left(lb+bh+lh\right)$ sq units
Lateral surface area $=\left[2\left(l+b\right)×h\right]$ sq units

(i) Length = 22 cm, breadth = 12 cm, height = 7.5 cm
Volume $=\left(Length×Breadth×Height\right)$ =
Total surface area $=2\left(lb+bh+lh\right)$
Lateral surface area $=\left[2\left(l+b\right)×h\right]$

(ii) Length = 15 m, breadth = 6 m, height = 9 dm = 0.9 m
Volume $=\left(Length×Breadth×Height\right)$ =
Total surface area$=2\left(lb+bh+lh\right)$
Lateral surface area $=\left[2\left(l+b\right)×h\right]$

(iii) Length = 24 m, breadth = 25 cm = 0.25 m, height = 6 m
Volume $=\left(Length×Breadth×Height\right)$ =
Total surface area$=2\left(lb+bh+lh\right)$
Lateral surface area $=\left[2\left(l+b\right)×h\right]$

(iv) Length = 48 cm = 0.48 m, breadth = 6 dm = 0.6 m, height = 1 m
Volume $=\left(Length×Breadth×Height\right)$ =
Total surface area $=2\left(lb+bh+lh\right)$
Lateral surface area $=\left[2\left(l+b\right)×h\right]$

Question 2:

The dimensions of a rectangular water tank are 2 m 75 cm by 1 m 80 cm by 1 m 40 cm. How many litres of water does it hold when filled to the brim?

Therefore, dimensions of the tank are:

∴ Volume =

Also, $1000c{m}^{3}=1L$

∴ Volume

Question 3:

A solid rectangular piece of iron measures 1.05 m × 70 cm × 1.5 cm. Find the weight of this piece in kilograms if 1 cm3 of iron weighs 8 grams.

$1m=100cm$
∴ Dimensions of the iron piece =
Total volume of the piece of iron
1 cm3 measures 8 gms.
∴Weight of the piece

Question 4:

The area of a courtyard is 3750 m2. Find the cost of covering it with gravel to a height of 1 cm if the gravel costs Rs 6.40 per cubic metre.

Volume of the gravel used
Cost of the gravel is Rs 6.40 per cubic meter.
∴ Total cost Rs 240

Question 5:

How many persons can be accommodated in a hall of length 16 m. breadth 12.5 m and height 4.5 m, assuming that 3.6 m3 of air is required for each person?

Total volume of the hall

It is given that  of air is required for each person.
The total number of persons that can be accommodated in that hall

Question 6:

A cardboard box is 1.2 m long, 72 cm wide and 54 cm high. How many bars of soap can be put into it if each bar measures 6 cm × 4.5 cm × 4 cm?

Volume of the cardboard box

Volume of each bar of soap

Total number of bars of soap that can be accommodated in that box bars

Question 7:

The size of a matchbox is 4 cm × 2.5 cm × 1.5 cm. What is the volume of a packet containing 144 matchboxes? How many such packets can be placed in a carton of size 1.5 m × 84 cm × 60 cm?

Volume occupied by a single matchbox

Volume of a packet containing 144 matchboxes

Volume of the carton

Total number of packets is a carton packets

Question 8:

How many planks of size 2 m × 25 cm × 8 cm can be prepared from a wooden block 5 m long, 70 cm broad and 32 cm thick, assuming that there is no wastage?

Total volume of the block

Total volume of each plank

∴ Total number of planks that can be made planks

Question 9:

How many bricks, each of size 25 cm × 13.5 cm × 6 cm, will be required to build a wall 8 m long, 5.4 m high and 33 cm thick?

Volume of the brick
Volume of the wall

Total number of bricks  bricks

Question 10:

A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring 22 cm × 12.5 cm × 7.5 cm. If $\frac{1}{12}$ of the total volume of the wall consists of mortar, how many bricks are there in the wall?

Volume of the wall
Total quantity of mortar
∴ Volume of the bricks

Volume of a single brick

∴ Total number of bricks bricks

Question 11:

Find the capacity of a rectangular cistern in litres whose dimensions are 11.2 m × 6 m × 5.8 m. Find the area of the iron sheet required to make the cistern.

Volume of the cistern litres

Area of the iron sheet required to make this cistern = Total surface area of the cistern

Question 12:

The volume of a block of gold is 0.5 m3. If it is hammered into a sheet to cover an area of 1 hectare, find the thickness of the sheet.

Volume of the block
We know:

Thickness

Question 13:

The rainfall recorded on a certain day was 5 cm. Find the volume of water that fell on a 2-hectare field.

Rainfall recorded = 5 cm = 0.05 m
Area of the field = 2 hectare =
Total rain over the field =

Question 14:

A river 2 m deep and 45 m wide is flowing at the rate of 3 km/h. Find the quantity of water that runs into the sea per minute.

Area of the cross-section of river

Rate of flow

Volume of water flowing through the cross-section in one minute  per minute

Question 15:

A pit 5 m long and 3.5 m wide is dug to a certain depth. If the volume of earth taken out of it is 14 m3, what is the depth of the pit?

Let the depth of the pit be d m.

But,
Given volume = 14 m3
∴ Depth  = 80 cm

Question 16:

A rectangular water tank is 90 cm wide and 40 cm deep. If it can contain 576 litres of water, what is its length?

Capacity of the water tank
Width = 90 cm = 0.9 m
Depth = 40 cm = 0.4 m

Length =

Question 17:

A beam of wood is 5 m long and 36 cm thick. It is made of 1.35 m3 of wood. What is the width of the beam?

Volume of the beam

Length = 5 m

Thickness = 36 cm = 0.36 m

Width =

Question 18:

The volume of a room is 378 m3 and the area of its floor is 84 m2. Find the height of the room.

Volume
Given:
Volume  = 378 m3
Area = 84 m2

∴ Height

Question 19:

A swimming pool is 260 m long and 140 m wide. If 54600 cubic metres of water is pumped into it, find the height of the water level in it.

Length of the pool = 260 m
Width of the pool = 140 m

Volume of water in the pool = 54600 cubic metres

∴ Height of water $=\frac{\text{volume}}{\text{length×width}}=\frac{54600}{260×140}=1.5$ metres

Question 20:

Find the volume of wood used to make a closed box of outer dimensions 60 cm × 45 cm × 32 cm, the thickness of wood being 2.5 cm all around.

External length = 60 cm
External width = 45 cm
External height = 32 cm

External volume of the box

Thickness of wood = 2.5 cm

∴  Internal length $=60-\left(2.5×2\right)=55$ cm
Internal width $=45-\left(2.5×2\right)=40$ cm
Internal height $=32-\left(2.5×2\right)=27$ cm

Internal volume of the box

Volume of wood = External volume - Internal volume

Question 21:

Find the volume of iron required to make an open box whose external dimensions are 36 cm × 25 cm × 16.5 cm, the box being 1.5 cm thick throughout. If 1 cm3 of iron weighs 8.5 grams, find the weight of the empty box in kilograms.

External length = 36 cm
External width = 25 cm
External height = 16.5 cm

External volume of the box

Thickness of iron = 1.5 cm

∴ Internal length $=36-\left(1.5×2\right)=33$ cm
Internal width $=25-\left(1.5×2\right)=22$ cm
Internal height  cm  (as the box is open)

Internal volume of the box

Volume of iron = External volume − Internal volume

Given:

Total weight of the box

Question 22:

A box with a lid is made of wood which is 3 cm thick. Its external length, breadth and height are 56 cm, 39 cm and 30 cm respectively. Find the capacity of the box. Also find the volume of wood used to make the box.

External length = 56 cm
External width = 39 cm
External height = 30 cm

External volume of the box

Thickness of wood = 3 cm

∴ Internal length $=56-\left(3×2\right)=50$ cm
Internal width $=39-\left(3×2\right)=33$ cm
Internal height $=30-\left(3×2\right)=24$ cm

Capacity of the box = Internal volume of the box

Volume of wood = External volume − Internal volume

Question 23:

The external dimensions of a closed wooden box are 62 cm, 30 cm and 18 cm. If the box is made of 2-cm-thick wood, find the capacity of the box.

External length = 62 cm
External width = 30 cm
External height = 18 cm

∴ External volume of the box

Thickness of the wood = 2 cm

Now, internal length $=62-\left(2×2\right)=58$ cm
Internal width $=30-\left(2×2\right)=26$ cm
Internal height $=18-\left(2×2\right)=14$ cm

∴ Capacity of the box = internal volume of the box

Question 24:

A closed wooden box 80 cm long, 65 cm wide and 45 cm high, is made of 2.5-cm-thick wood. Find the capacity of the box and its weight if 100 cm3 of wood weighs 8 g.

External length = 80 cm
External width = 65 cm
External height = 45 cm

∴ External volume of the box

Thickness of the wood = 2.5 cm

Then internal length$=80-\left(2.5×2\right)=75$ cm
Internal width $=65-\left(2.5×2\right)=60$ cm
Internal height $=45-\left(2.5×2\right)=40$ cm

Capacity of the box = internal volume of the box

Volume of the wood = external volume − internal volume

It is given that

∴ Weight of the wood

Question 25:

Find the volume, lateral surface area and the total surface area of a cube each of whose edges measures:
(i) 7 m
(ii) 5.6 cm
(iii) 8 dm 5 cm

(i) Length of the edge of the cube = a = 7 m
Now, we have the following:
​Volume
Lateral surface area
Total Surface area

(ii) Length of the edge of the cube = a = 5.6 cm
​Now, we have the following:
Volume
Lateral surface area
Total Surface area

(iii) Length of the edge of the cube = a = 8 dm 5 cm = 85 cm
​Now, we have the following:
Volume
Lateral surface area
Total Surface area

Question 26:

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

Let a be the length of the edge of the cube.
Total surface area

∴ Volume

Question 27:

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

Let a be the length of the edge of the cube.

Then volume

Also,

∴ Surface area

Question 28:

The dimensions of a metal block are 2.25 m by 1.5 m by 27 cm. It is melted and recast into cubes, each of side 45 cm. How many cubes are formed?

1 m = 100 cm
Volume of the original block

Length of the edge of one cube = 45 cm
Then volume of one cube

∴ Total number of blocks that can be cast

Question 29:

If the length of each edge of a cube is doubled, how many times does its volume become? How many times does its surface area become?

Let a be the length of the edge of a cube.
Volume of the cube$={a}^{3}$
Total surface area$=6{a}^{2}$

If the length is doubled, then the new length becomes 2a.
Now, new volume $=\left(2a{\right)}^{3}=8{a}^{3}$
Also, new surface area=$=6\left(2a{\right)}^{2}=6×4{a}^{2}=24{a}^{2}$
∴ The volume is increased by a factor of 8, while the surface area increases by a factor of 4.

Question 30:

A solid cubical block of fine wood costs Rs 256 at Rs 500 per m2. Find its volume and the length of each side.

Cost of wood = Rs $500/{\mathrm{m}}^{3}$

Cost of the given block = Rs 256

∴ Volume of the given block

Also, length of its edge = a  = 80 cm

Question 1:

Find the volume, curved surface area and total surface area of each of the cylinders whose dimensions are:
(i) radius of the base = 7 cm and height = 50 cm
(ii) radius of the base = 5.6 m and height = 1.25 m
(iii) radius of the base = 14 dm and height = 15 m

Volume of a cylinder =
Lateral surface$=2\mathrm{\pi }rh$
Total surface area $=2\mathrm{\pi }r\left(h+r\right)$

(i) Base radius = 7 cm; height = 50 cm
Now, we have the following:
Volume
Lateral surface area$=2\mathrm{\pi }rh$
Total surface area $=2\mathrm{\pi }r\left(h+r\right)$

(ii) Base radius = 5.6 m; height = 1.25 m
Now, we have the following:
Volume
Lateral surface area$=2\mathrm{\pi }rh$
Total surface area $=2\mathrm{\pi }r\left(h+r\right)$

(iii) Base radius = 14 dm = 1.4 m, height = 15 m
Now, we have the following:
Volume
Lateral surface area$=2\mathrm{\pi }rh$
Total surface area $=2\mathrm{\pi }r\left(h+r\right)$

Question 2:

A milk tank is in the form of a cylinder whose radius is 1.5 m and height is 10.5 m. Find the quantity of milk in litres that can be stored in the tank.

Question 3:

A wooden cylindrical pole is 7 m high and its base radius is 10 cm. Find its weight if the wood weighs 225 kg per cubic metre.

Height = 7 m
Radius = 10 cm = 0.1 m
Volume
Weight of wood = 225 kg/m3
∴ Weight of the pole

Question 4:

Find the height of the cylinder whose volume is 1.54 m3 and diameter of the base is 140 cm?

Diameter = 2r = 140 cm
i.e., radius, r = 70 cm = 0.7 m

Now, volume ​

Question 5:

The volume of a circular iron rod of length 1 m is 3850 cm3. Find its diameter.

Volume
Height = 1 m =100 cm

Question 6:

A closed cylindrical tank of diameter 14 m and height 5 m is made from a sheet of metal. How much sheet of metal will be required?

Diameter = 14 m
Height = 5 m

∴ Area of the metal sheet required = total surface area

Question 7:

The circumference of the base of a cylinder is 88 cm and its height is 60 cm. Find the volume of the cylinder and its curved surface area.

Circumference of the base = 88 cm
Height = 60 cm

Area of the curved surface
Circumference
∴ Volume

Question 8:

The lateral surface area of a cylinder of length 14 m is 220 m2. Find the volume of the cylinder.

Length = height = 14 m
Lateral surface area
∴ Volume

Question 9:

The volume of a cylinder of height 8 cm is 1232 cm3. Find its curved surface area and the total surface area.

Height = 8 cm
Volume
Now, radius$=r=\sqrt{\frac{1232}{\mathrm{\pi h}}}=\sqrt{\frac{1232×7}{22×8}}=\sqrt{49}=7cm$
Also, curved surface area
∴ Total surface area

Question 10:

The radius and height of a cylinder are in the ratio 7 : 2. If the volume of the cylinder is 8316 cm3, find the total surface area of the cylinder.

We have: $\frac{radius}{height}=\frac{7}{2}$
i.e., $r=\frac{7}{2}h$
Now, volume

Then
∴ Total surface area

Question 11:

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

Curved surface area
Circumference
Now, height

Also, radius, $r=\frac{4400}{2\mathrm{\pi h}}=\frac{4400×7}{2×22×40}=\frac{35}{2}$

∴ Volume

Question 12:

A particular brand of talcum powder is available in two packs, a plastic can with a square base of side 5 cm and of height 14 cm, or one with a circular base of radius 3.5 cm and of height 12 cm. Which of them has greater capacity and by how much?

For the cubic pack:
Length of the side, a = 5 cm
Height = 14 cm
Volume

For the cylindrical pack:
Height = 12 cm
Volume

We can see that the pack with a circular base has a greater capacity than the pack with a square base.
Also, difference in volume

Question 13:

Find the cost of painting 15 cylindrical pillars of a building at Rs 2.50 per square metre if the diameter and height of each pillar are 48 cm and 7 metres respectively.

Diameter = 48 cm
Radius = 24 cm = 0.24 m
Height = 7 m

Now, we have:
Lateral surface area of one pillar
Surface area to be painted = total surface area of 15 pillars
∴ Total cost

Question 14:

A rectangular vessel 22 cm by 16 cm by 14 cm is full of water. If the total water is poured into an empty cylindrical vessel of radius 8 cm, find the height of water in the cylindrical vessel.

Volume of the rectangular vessel
Radius of the cylindrical vessel = 8 cm
Volume$={\mathrm{\pi r}}^{2}\mathrm{h}$

As the water is poured from the rectangular vessel to the cylindrical vessel, we have:
Volume of the rectangular vessel  = volume of the cylindrical vessel

∴ Height of the water in the cylindrical vessel

Question 15:

A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 11 cm. It is drawn out into a wire of diameter 1 mm. What will be the length of the wire so obtained?

Diameter of the given wire = 1 cm
Length = 11 cm
Now, volume
The volumes of the two cylinders would be the same.
Now, diameter of the new wire = 1 mm = 0.1 cm
∴ New length  ≅ 11 m

Question 16:

A solid cube of metal each of whose sides measures 2.2 cm is melted to form a cylindrical wire of radius 1 mm.  Find the length of the wire so obtained.

Length of the edge, a = 2.2 cm
Volume of the cube
Volume of the wire$={\mathrm{\pi r}}^{2}\mathrm{h}$
Radius = 1 mm = 0.1 cm
As volume of cube = volume of wire, we have:

Question 17:

How many cubic metres of earth must be dug out to sink a well which is 20 m deep and has a diameter of 7 metres? If the earth so dug out is spread over a rectangular plot 28 m by 11 m, what is the height of the platform so formed?

Diameter = 7 m
​Depth = 20 m

​Volume of the earth dug out
Volume of the earth piled upon the given plot

Question 18:

A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of the embankment so formed.

Inner diameter = 14 m
Depth = 12 m
​Volume of the earth dug out

Width of embankment = 7 m

Since volume of embankment = volume of earth dug out, we have:

∴ Height of the embankment = 4 m

Question 19:

A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of the road roller is 84 cm and its length is 1 m.

Diameter = 84 cm
Length = 1 m = 100 cm
Now, lateral surface area

Question 20:

A cylinder is open at both ends and is made of 1.5-cm-thick metal. Its external diameter is 12 cm and height is 84 cm. What is the volume of metal used in making the cylinder? Also, find the weight of the cylinder if 1 cm3 of the metal weighs 7.5 g.

Thickness of the cylinder = 1.5 cm
External diameter = 12 cm
also, internal radius = 4.5 cm
Height = 84 cm

Now, we have the following:
Total volume
Inner volume
Now, volume of the metal = total volume − inner volume
∴ Weight of iron    [Given: ]

Question 21:

The length of a metallic tube is 1 metre, its thickness is 1 cm and its inner diameter is 12 cm. Find the weight of the tube if the density of the metal is 7.7 grams per cubic centimetre.

Length = 1 m = 100 cm
Inner diameter = 12 cm
Now, inner volume
Thickness = 1 cm

Now, we have the following:
Total volume
Volume of the tube
Density of the tube = 7.7 g/cm3
∴ Weight of the tube

Question 1:

The maximum length of a pencil that can be kept in a rectangular box of dimensions 12 cm × 9 cm × 8 cm, is
(a) 13 cm
(b) 17 cm
(c) 18 cm
(d) 19 cm

(b) 17

Length of the diagonal of a cuboid $=\sqrt{{l}^{2}+{b}^{2}+{h}^{2}}$

Question 2:

The total surface area of a cube is 150 cm2. Its volume is
(a) 216 cm3
(b) 125 cm3
(c) 64 cm3
(d) 1000 cm3

(b)

Total surface area , where a is the length of the edge of the cube.
$⇒6{a}^{2}=150$

∴ Volume

Question 3:

The volume of a cube is 343 cm3. Its total surface area is
(a) 196 cm2
(b) 49 cm2
(c) 294 cm2
(d) 147 cm2

(c)

Volume

∴ Total surface area

Question 4:

The cost of painting the whole surface area of a cube at the rate of 10 paise per cm2 is Rs 264.60. Then, the volume of the cube is
(a) 6859 cm3
(b) 9261 cm3
(c) 8000 cm3
(d) 10648 cm3

(b)

Rate of painting = 10 paise per sq cm = Rs 0.1/cm2
Total cost = Rs 264.60
Now, total surface area
Also, length of edge, a

Question 5:

How many bricks, each measuring 25 cm × 11.25 cm × 6 cm, will be needed to build a wall 8 m long, 6 m high and 22.5 cm thick?
(a) 5600
(b) 6000
(c) 6400
(d) 7200

(c) 6400

Volume of each brick
Volume of the wall
∴  No. of bricks =

Question 6:

How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
(a) 10
(b) 100
(c) 1000
(d) 10000

(c) 1000

Volume of the smaller cube
Volume of box     [1 m = 100 cm]
∴ Total no. of cubes $=\frac{100×100×100}{10×10×10}=1000$

Question 7:

The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm2. The volume of the cuboid is
(a) 48 cm3
(b) 64 cm3
(c) 96 cm3
(d) 120 cm3

(a)

Let a be the length of the smallest edge.
Then the edges are in the proportion a : 2a : 3a.
Now, surface area
$⇒a=\sqrt{\frac{88}{22}}=\sqrt{4}=2$
Also, 2a = 4 and 3a = 6
∴ Volume

Question 8:

Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is
(a) 1 : 3
(b) 1 : 9
(c) 1 : 27
(d) none of these

(b) 1: 9

Question 9:

The surface area of a (10 cm × 4 cm × 3 cm) brick is
(a) 84 cm2
(b) 124 cm2
(c) 164 cm2
(d) 180 cm2

(c) 164 sq cm

Surface area

Question 10:

An iron beam is 9 m long, 40 cm wide and 20 cm high. If 1 cubic metre of iron weighs 50 kg, what is the weight of the beam?
(a) 56 kg
(b) 48 kg
(c) 36 kg
(d) 27 kg

(c) 36 kg

Volume of the iron beam
∴ Weight

Question 11:

A rectangular water reservoir contains 42000 litres of water. If the length of reservoir is 6 m and its breadth is 3.5 m, the depth of the reservoir is
(a) 2 m
(b) 5 m
(c) 6 m
(d) 8 m

(a) 2 m

42000 L = 42 m3
$\mathrm{Volume}=lbh$

Question 12:

The dimensions of a room are (10 m × 8 m × 3.3 m). How many men can be accommodated in this room if each man requires 3 m3 of space?
(a) 99
(b) 88
(c) 77
(d) 75

(b) 88

Volume of the room
One person requires 3 m3.
∴ Total no. of people that can be accommodated$=\frac{264}{3}=88$

Question 13:

A rectangular water tank is 3 m long, 2 m wide and 5 m high. How many litres of water can it hold?
(a) 30000
(b) 15000
(c) 25000
(d) 35000

(a) 30000

Question 14:

The area of the cardboard needed to make a box of size 25 cm × 15 cm × 8 cm will be
(a) 390  cm2
(b) 1390 cm2
(c) 2780 cm2
(d) 1000 cm2

(b)

Surface area

Question 15:

The diagonal of a cube measures $4\sqrt{3}$ cm. Its volume is
(a) 8 cm3
(b) 16 cm3
(c) 27 cm3
(d) 64 cm3

(d)

Diagonal of the cube
i.e., a = 4 cm
∴ Volume

Question 16:

The diagonal of a cube is $9\sqrt{3}$ cm long. Its total surface area is
(a) 243 cm2
(b) 486 cm2
(c) 324 cm2
(d) 648 cm2

(b) 486 sq cm

Diagonal
i.e., a = 9
∴ Total surface area

Question 17:

If each side of a cube is doubled then its volume
(a) is doubled
(b) becomes 4 times
(c) becomes 6 times
(d) becomes 8 times

(d) If each side of the cube is doubled, its volume becomes 8 times the original volume.

Let the original side be a units.
Then original volume = a3 cubic units
Now, new side  = 2a units
Then new volume = (2a)3 sq units = 8 a3cubic units
Thus, the volume becomes 8 times the original volume.

Question 18:

If each side of a cube is doubled, its surface area
(a) is doubled
(b) becomes 4 times
(c) becomes 6 times
(d) becomes 8 times

(b) becomes 4 times.

Let the side of the cube be a units.
Surface area = 6a2 sq units
Now, new side = 2a units
New surface area = 6(2a2 ) sq units = 24a2 sq units.
Thus, the surface area becomes 4 times the original area.

Question 19:

Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. The edge of the new cube formed is
(a) 12 cm
(b) 14 cm
(c) 16 cm
(d) 18 cm

(a) 12 cm

Total volume
∴ Edge of the new cube

Question 20:

Five equal cubes, each of edge 5 cm, are placed adjacent to each other. The volume of the cuboid so formed, is
(a) 125 cm3
(b) 375 cm3
(c) 525 cm3
(d) 625 cm3

(d)

Length of the cuboid so formed = 25 cm
Breadth of the cuboid = 5 cm
Height of the cuboid = 5 cm
∴ Volume of cuboid

Question 21:

A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out?
(a) 32 m3
(b) 36 m3
(c) 40 m3
(d) 44 m3

(d) 44 m3

Diameter = 2 m
Height = 14 m

Question 22:

If the capacity of a cylindrical tank is 1848 m3 and the diameter of its base is 14 m, the depth of the tank is
(a) 8 m
(b) 12 m
(c) 16 m
(d) 18 m

(b) 12 m

Diameter = 14 m
Volume = 1848 m3

Question 23:

The ratio of the total surface area to the lateral surface area of a cylinder whose radius is 20 cm and height 60 cm, is
(a) 2 : 1
(b) 3 : 2
(c) 4 : 3
(d) 5 : 3

(c) 4 : 3

Question 24:

The number of coins, each of radius 0.75 cm and thickness 0.2 cm, to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is
(a) 460
(b) 500
(c) 600
(d) 640

(d) 640

Question 25:

66 cm3 of silver is drawn into a wire 1 mm in diameter. The length of the wire will be
(a) 78 m
(b) 84 m
(c) 96 m
(d) 108 m

(b) 84 m

Question 26:

The height of a cylinder is 14 cm and its diameter is 10 cm. The volume of the cylinder is
(a) 1100 cm3
(b) 3300 cm3
(c) 3500 cm3
(d) 7700 cm3

(a) 1100 cm3
Volume

Question 27:

The height of a cylinder is 80 cm and the diameter of its base is 7 cm. The whole surface area of the cylinder is
(a) 1837 cm2
(b) 1760 cm2
(c) 1942 cm2
(d) 3080 cm2

(a) 1837 cm2
Diameter = 7 cm
Height = 80 cm
∴ Total surface area

Question 28:

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

(b) 396 cm3
Here, curved surface area

Question 29:

The diameter of a cylinder is 14 cm and its curved surface area is 220 cm2. The volume of the cylinder is
(a) 770 cm3
(b) 1000 cm3
(c) 1540 cm3
(d) 6622 cm3

(a) 770 cm3
Diameter = 14 cm
Now, curved surface area

Question 30:

The ratio of the radii of two cylinders is 2 : 3 and the ratio of their heights is 5 : 3. The ratio of their volumes will be
(a) 4 : 9
(b) 9 : 4
(c) 20 : 27
(d) 27 : 20

(c) 20:27

Question 1:

Find the volume of a cube whose total surface area is 384 cm2.

Total surface area$=6{a}^{2}$
$⇒6{a}^{2}=384$

Question 2:

How many soap cakes each measuring 7 cm × 5 cm × 2.5 cm can be placed in a box of size 56 cm × 40 cm × 25 cm?

Volume of a soap cake
Volume of the box

No. of soap cakes

∴ 640 cakes of soap can be placed in a box of the given size.

Question 3:

The radius and height of a cylinder are in the ratio 5 : 7 and its volume is 550 cm3. Find its radius and height.

$\frac{\mathrm{Radius}}{\mathrm{height}}=\frac{r}{h}=\frac{5}{7}\phantom{\rule{0ex}{0ex}}⇒r=\frac{5}{7}h$
Now, volume

Question 4:

Find the number of coins, 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder with a height of 10 cm and a diameter of 4.5 cm.

Volume of the coin$={\mathrm{\pi r}}^{2}\mathrm{h}=\frac{22}{7}×0.75×0.75×0.2$
Volume of the cylinder $={\mathrm{\pi r}}^{2}\mathrm{h}=\frac{22}{7}×2.25×2.25×10$
No. of coins

∴ 450 coins must be melted to form the required cylinder.

Question 5:

Find the surface area of a chalk box, whose length, breadth and height are 18 cm, 10 cm and 8 cm respectively.

Length = 18 cm
Height = 8 cm
∴ Total surface area

Question 6:

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

Curved surface area

Volume

Now, $r=\frac{132}{\mathrm{\pi h}}=\frac{132×7}{22×6}=7m$

i.e., diameter of the pillar,

Question 7:

Mark (✓) against the correct answer:
The circumference of the circular base of a cylinder is 44 cm and its height is 15 cm. The volume of the cylinder is
(a) 1155 cm3
(b) 2310 cm3
(c) 770 cm3
(d) 1540 cm3

(b) 2310 cm3

Height = 15 cm
Circumference

∴ Volume

Question 8:

Mark (✓) against the correct answer:
the area of the base of a circular cylinder is 35 cm2 and its height is 8 cm. The volume of the cylinder is
(a) 140 cm3
(b) 280 cm3
(c) 420 cm3
(d) 210 cm3

(b) 280 cm3
Area = 35 cm2
Height = 8 cm

Question 9:

Mark (✓) against the correct answer:
A cuboid having dimensions 16 m × 11 m × 8 m is melted to form a cylinder of radius 4 m. What is the height of the cylinder?
(a) 28 m
(b) 14 m
(c) 21 m
(d) 32 m

(a) 28 m
Volume of the cuboid
​Volume of the cylinder

Question 10:

Mark (✓) against the correct answer:
The dimensions of a cuboid are 8 m  6 m  4 m. Its lateral surface area is
(a) 210 m2
(b) 105 m2
(c) 160 m2
(d) 240 m2

Lateral surface area

Question 11:

Mark (✓) against the correct answer:
The length, breadth and height of a cuboid are in the ratio 3 : 4 : 6 and its volume is 576 cm3. The whole surface area of the cuboid is
(a) 216 cm2
(b) 324 cm2
(c) 432 cm2
(d) 460 cm2

(c) 432 sq cm
Volume
$⇒x=\sqrt{\frac{576}{72}}=2$
∴ Total surface area

Question 12:

Mark (✓) against the correct answer:
The surface area of a cube is 384 cm2. Its volume is
(a) 512 cm3
(b) 256 cm3
(c) 384 cm3
(d) 320 cm3

(a) 512 cm3
Surface area$=6{a}^{2}$
$⇒6{a}^{2}=384$

∴ Volume

Question 13:

Fill in the blanks.
(i) If l, b, h be the length, breadth and height of a cuboid, then its whole surface area = (.......) sq units.
(ii) If l, b, h be the length, breadth and height of a cuboid, then its lateral surface area = (.......) sq units.
(iii) If each side of a cube is a, then its lateral surface area is ....... sq units.
(iv) If r is the radius of the base and h be the height of a cylinder, then its volume is (.......) cubic units.
(v) If r is the radius of the base and h be the height of a cylinder, then its lateral surface area is (......) sq units.

(i) If l, b and h are the length, breadth and height of a cuboid, respectively, then its whole surface area is equal to $2\left(lb+lh+bh\right)$ sq units.
(ii) If l, b and h are the length, breadth and height of a cuboid, respectively, then its lateral surface area is equal to $2\left(\left(l+b\right)×h\right)$ sq units.
(iii) If each side of a cube is a, then the lateral surface area is $4{a}^{2}$ sq units.
(iv) If r and h are the radius of the base and height of a cylinder, respectively, then its volume is $\mathrm{\pi }{r}^{2}h$ cubic units.
(v) If r and h are the radius of the base and height of a cylinder, then its lateral surface area is $2\mathrm{\pi }rh$ sq units.