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Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km/hr, then in how much time will the tank be filled completely?

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Solution

We have,Internal radius of the pipe, r=202=10 cm=0.1 m,Radius of the cylindrical tank, R=102=5 m andHeight of the cylindrical tank, H=2 mAlso, the speed of the water flow in the pipe, h=4 km/hr=4×1000 m1 hr=4000 m/hrNow,The volume of the water flowing out of the pipe in a hour=πr2h=227×0.1×0.1×4000=8807 m3And,The volume of the cylindrical tank=πR2H=227×5×5×2=11007 m3So,The time taken to fill the tank=Volume of the cylindrical tankVolume of water flowing out of the pipe in a hour=110078807=1100880=54 hr=114 hr=1 hr and 14×60 min=1 hr 15 min

So, the tank will be completely filled in 1 hour 15 minutes.

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