Exercise: Volume And Surface Area

Questions for: Volume And Surface Area

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: B

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

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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: B

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.

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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: A
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.
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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: C

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.

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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: B

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

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