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Question

A farmer connects a pipe of internal diameter 20 cm form a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 kilometer per hour, in how much time will the tank be filled?

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Solution

Radius (r1) of circular end of pipe =20200=0.1 m

Area of cross-section =π×r21=π×(0.1)2=0.01π sq. m

Speed of water =3 kilometer per hour = 300060=50 meter per minute.

Volume of water that flows in 1 minute from pipe = 50×0.01π=0.5π cu. m

From figure 2, Volume of water that flows in t minutes from pipe = t×0.5π cu. m

Radius (r2) of circular end of cylindrical tank = 102=5 m

Depth (h2) of cylindrical tank =2 m

Let the tank be filled completely in t minutes.

The volume of water filled in tank in t minutes is equal to the volume of water flowed in t minutes from the pipe.

Volume of water that flows in t minutes from pipe = Volume of water in tank

Therefore, t×0.5π=πr22×h2

t×0.5=52×2

t=25×20.5

t=100

Therefore, the cylindrical tank will be filled in 100 minute.

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