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Q.

Water is flowing through a cylindrical pipe of internal diameter 2cm, into a cylindrical tank of base radius 40 cm at the rate of 0.7m/sec. By how much will the water rise in the tank in half an hour?

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a

78.75 cm

b

85 cm

c

80.75 cm

d

75 cm

answer is A.

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Detailed Solution

Given that, water is flowing through a cylindrical pipe of internal diameter 2cm, into a cylindrical tank of base radius 40 cm at the rate of 0.7m/sec.
Let rise in water level be h m.
Now, Volume of water through a pipe in 30 minutes = Volume of tank.
Pipe is in form of a Cylinder whose diameter = 2cm.
So,

Radius = Diameter 2 = 22 = 1 cm = 1100 m

Now, Rate of filling water is

0.7 m / sec

. So, in 1 second, water flowing through pipe

= 0.7 m

. Given water flowing through a pipe in 30 minutes. So, the water filled is

= 0.7 × 30 × 60 = 1260 m

Thus, height of cylindrical Pipe

1260 m

.
We know that, volume of the cylinder

= π r 2 h

.

= π r 2 h = π (1 / 100) 2 × 1260 = π × 1 / 100 × 1 / 100 × 1260 = π × 126 1000 m 3

Let us find the radius of the tank.

r = 40 cm = 40100 m = 410 m

Volume of Tank

V = π r 2 h = π × 4102 × h = 16 π h 100 m 3

Volume Of Pipe = Volume of Tank
Question Image

Question Image

The height of the water in the tank in half an hour is 78.75 cm.
The correct option is (1).

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