Volume Calculation Aptitude Questions

Q1 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:

Solution

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

Volume =

1

r2h =

1

x

x 32 x 4

cm3

= 12

cm3

Q2 In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

Solution

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.
			20

Q3 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:

Solution

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

Q4 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

Solution

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

Q5 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:

Solution

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.

Q6 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:

Solution

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.

Q7 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:

Solution

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

Q8 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:

Solution

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.

Q9 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:

Solution

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.

Q10 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:

Solution

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.