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Question

Water flows at the rate of 10m/minute through a cylindrical pipe 5mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40cm and depth 24cm?

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Solution

Radius of the pipe =52 mm=52×110 cm=14 cm

Speed of water =10m/min=1000 cm/min
Volume of water that flows in 1 minute =πr2h
=227×14×14×1000
=13757 cm3
Radius of conical vessel =402=20 cn
Depth =24 cm
So,
Capacity of the vessel =13×πr2h
=13×227×20×20×24
=704007 cm3
Therefore,
Time required to fill vessel =Capacity of the vesselVolume of water flowing per minute
=70400/71375/7
=2655 minutes
=51 min 12 sec


Hence, It takes 51 min 12 sec to fill a conical vessel.


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