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Question

A farmer connects a pipe of internal diameter 20cm form a canal into a cylindrical tank in her field, which is 10m in diameter and 2m deep.

If water flows through the pipe at the rate of 3km/hr, in how much time will the tank be filled?


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Solution

Step 1:Finding out the volume of water flowing and that of cylindrical tank.

Radius of Cylindrical tank (r)=5m=500cm[Sinceradius=diameter2,1m=100cm]

Depth of Cylindrical tank (h)=2m=200cm

Speed of water flows in pipe =3km/hr=(3,000m/hr)[1km=1000m]

Volume of water flows in 1hr=πr2h=π×10×10×300000cm3

Volume of cylindrical tank =πr2h=π×500×500×200cm3

Step 2 : Finding the time taken to fill the tank.

Timetakentofillthetank=Volumeofcylindricaltank÷Volumeofwaterflowin1hr

t×(30π)=πr2ht×(30π)=π×52×2t=5x5x230t=53hourst=53×60mins[Since1hr=60mins]t=100minutest=1hour40minutes

Hence, The time required to fill the tank is 1hour40minutes.


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