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Question

A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field, which is 12 m in diameter and 2.5 m deep. If water flows through the pipe at the rate of 3.6 km/hr, then in how much time will the tank be filled? Also, find the cost of water if the canal department charges at the rate of 0.07 per m3. [CBSE 2009C]

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Solution

We have,the radius of the cylindrical tank, R=122=6 m=600 cm,the depth of the tank, H=2.5 m=250 cm,the radius of the cylindrical pipe, r=252=12.5 cm,speed of the flowing water, h=3.6 km/h=360000 m3600 s=100 cm/sNow,Volume of water flowing out from the pipe in a hour=πr2h=227×12.5×12.5×100 cm3Also,Volume of the tank=πR2H=227×600×600×250 cm3So, the time taken to fill the tank=Volume of the tankVolume of water flowing out from the pipe in a hour=227×600×600×250227×12.5×12.5×100=5760 s=57603600=1.6 hAlso, the cost of water=0.07×227×6×6×2.5=19.80


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