Volume And Surface Area

Question: 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.
			20

Video Explanation: https://youtu.be/dDbVuBzYop8

Question:
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.

Question: 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.