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Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 meters per second into a cylindrical tank, the radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes.

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answer is C.

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Detailed Solution

Given, internal diameter of pipe=2 cm.
So the internal radius of pipe = 1 cm =0.01 m
Water is flowing at rate of 6 m/s into cylindrical tank.
Time=30 minutes
We know that 1minute=60 seconds.
30 minutes=30

×

60=1800 seconds.
Volume of water from circular pipe will be given by

π r 2 ×

rate

×

time.

Volume of water that flowing out in 1800 seconds from pipe = 227 × 0.01 × 0.01 × 6 × 1800

.
Let the rise of the water in the tank be

h

m.
The radius of the base =60 cm = 0.6 m.

Volume of water in tank in 30 minutes = 227 × 0.6 × 0.6 × h

The volume of the water in the tank = the volume of the water from the circular pipe.

227 × 0.6 × 0.6 × h = 227 × 0.01 × 0.01 × 6 × 1800

h = 0.01 × 0.01 × 6 × 1800 0.6 × 0.6

h = 3

m
Therefore, the rise in the water is 3 m.
Therefore, the correct option is 3.

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