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Aptitude Topics

Volume and Surface Area

 
1

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
A. 12 cm3
B. 15 cm3
C. 16 cm3
D. 20 cm3

Answer: Option A

Explanation:

Clearly, we have r = 3 cm and h = 4 cm.

 

 Volume = 1 r2h = 1 x  x 32 x 4 cm3 = 12 cm3.
3 3

 

 
2

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A. 75 cu. m
B. 750 cu. m
C. 7500 cu. m
D. 75000 cu. m

Answer: Option B

Explanation:

1 hectare = 10,000 m2

So, Area = (1.5 x 10000) m2 = 15000 m2.

 

Depth = 5 m = 1 m.
100 20

 

 

 Volume = (Area x Depth) = 15000 x 1 m3 = 750 m3.

 

 
3

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
A. 720
B. 900
C. 1200
D. 1800

Answer: Option C

Explanation:

2(15 + 12) x h = 2(15 x 12)

 

 h = 180 m = 20 m.
27 3

 

 

 Volume = 15 x 12 x 20 m3 = 1200 m3.
3

 

 
4

66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
A. 84
B. 90
C. 168
D. 336

Answer: Option A

Explanation:

Let the length of the wire be h.

 

Radius = 1 mm = 1 cm. Then,
2 20

 

 

22 x 1 x 1 x h = 66.
7 20 20

 

 

 h = 66 x 20 x 20 x 7 = 8400 cm = 84 m.
22

 

 
5

A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:
A. 3.6 kg
B. 3.696 kg
C. 36 kg
D. 36.9 kg

Answer: Option B

Explanation:

External radius = 4 cm,

Internal radius = 3 cm.

 

Volume of iron
= 22 x [(4)2 - (3)2] x 21 cm3
7
 
= 22 x 7 x 1 x 21 cm3
7
  = 462 cm3.

 

 Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.

 

 
6

A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:
A. 12 kg
B. 60 kg
C. 72 kg
D. 96 kg

Answer: Option B

Explanation:

 

Volume of water displaced = (3 x 2 x 0.01) m3
  = 0.06 m3.

 

 

 Mass of man = Volume of water displaced x Density of water
  = (0.06 x 1000) kg
  = 60 kg.

 

 
7

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:
A. 20 cm
B. 25 cm
C. 35 cm
D. 50 cm

Answer: Option B

Explanation:

Total volume of water displaced = (4 x 50) m3 = 200 m3.

 

 Rise in water level = 200 m 0.25 m = 25 cm.
40 x 20

 

 

 
8

The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
A. 30 m2
B. 40 m2
C. 60 m2
D. 80 m2

Answer: Option C

Explanation:

l = 10 m,

h = 8 m.

So, r = √(l2 - h2 )= √((10)2 - 82 )= 6 m.

 Curved surface area = rl = ( x 6 x 10) m2 = 60 m2.

 
9

A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
A. 49 m2
B. 50 m2
C. 53.5 m2
D. 55 m2

Answer: Option A

Explanation:

Area of the wet surface = [2(lb + bh + lh) - lb]
  = 2(bh + lh) + lb
  = [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2
  = 49 m2.
 
10

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:
A. 4830
B. 5120
C. 6420
D. 8960

Answer: Option B

Explanation:

Clearly, l = (48 - 16)m = 32 m,

b = (36 -16)m = 20 m,

h = 8 m.

 Volume of the box = (32 x 20 x 8) m3 = 5120 m3.

 

 
11

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
A. 3 : 7
B. 7 : 3
C. 6 : 7
D. 7 : 6

Answer: Option B

Explanation:

 

r2h = 924          r = 924 x 2 = 7 m.
2rh 264 264

 

 

And, 2rh = 264          h = 264 x 7 x 1 x 1 = 6m.
22 2 7

 

 

 Required ratio = 2r = 14 = 7 : 3.
h 6

 

 
12

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:
A. 90 cm
B. 1 dm
C. 1 m
D. 1.1 cm

Answer: Option B

Explanation:

Let the thickness of the bottom be x cm.

Then, [(330 - 10) x (260 - 10) x (110 - x)] = 8000 x 1000

 320 x 250 x (110 - x) = 8000 x 1000

 

 (110 - x) = 8000 x 1000 = 100
320 x 250

 

 x = 10 cm = 1 dm.

 
13

What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
A. 344.35 cm2
B. 462 cm2
C. 498.35 cm2
D. None of these

Answer: Option C

Explanation:

h = 14 cm, r = 7 cm.

So, l = √((7)2 + (14)2 )= √245=7√5 cm.

 

 Total surface area = rl + r2
 
= 22 x 7 x 7√5 + 22 x 7 x 7 cm2
7 7
  = [154(√5 + 1)] cm2
  = (154 x 3.236) cm2
  = 498.35 cm2.

 

 
14

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
A. 2 : 1
B. 3 : 2
C. 25 : 18
D. 27 : 20

Answer: Option C

Explanation:

Volume of the large cube = (33 + 43 + 53) = 216 cm3.

Let the edge of the large cube be a.

So, a3 = 216          a = 6 cm.

 

 Required ratio = 6 x (32 + 42 + 52) = 50 = 25 : 18.
6 x 62 36

 

 
15

 

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
A. 5600
B. 6000
C. 6400
D. 7200

Answer: Option C

Explanation:

 

Number of bricks = Volume of the wall = 800 x 600 x 22.5 = 6400.
Volume of 1 brick 25 x 11.25 x 6