Volume And Surface Area

Question:
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.

Question: 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

Video Explanation: https://youtu.be/Njsid2mVwUY

Question:
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.

Question:
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

Question:
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

Question: 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.

Question:
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.

Question: 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

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

Question:
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

Question:
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