Volume And Surface Area

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: B

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.

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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: B

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.

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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: A

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

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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: C

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

Video Explanation: https://youtu.be/V8EQ1YIaH74

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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: B

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

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Questions for: Volume And Surface Area