volume and surface area

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6. 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.
7. 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
8. 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.
9. 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.
10. 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.
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