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 =52mm=52×110cm=14cm
Speed of water =10m/min=1000cm/min
Volume of water that flows in 1 minute =πr2h
=227×14×14×1000
=13757cm3
Radius of conical vessel =402=20cn
Depth =24cm
So,
Capacity of the vessel =13×πr2h
=13×227×20×20×24
=704007cm3
Therefore,
Time required to fill vessel =CapacityofthevesselVolumeofwaterflowingperminute
=70400/71375/7
=2655minutes
=51min12sec
Hence, It takes 51min12sec to fill a conical vessel.