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Question
Water flows at the rate of 15 m per minute through a cylindrical pipe, having the diameter 20 mm. How much time will it take to fill a conical vessel of base diameter 40 cm and depth 45 cm?
Solution
Diameter of a pipe = 20 mm ….(given)
Radius of the pipe = `20/2` mm = 10 mm = 1 cm
Speed of water = 15 m/min= 1500 cm/min
Volume of cylinder = πr2 h
Volume of water that flows in pipe in 1 minute
= `22/7xx1^2xx1500`
= `33000/7"cm"^3`
Radius of conical vessel = `40/2` = 20 cm
Depth 45 cm ... Given
Capacity of the conical vessel
`=1/3pir^2h`
=`1/3xx22/7xx20xx20xx45`
`=396000/21"cm"^3`
Time required to fill the vessel `="Capacity of the vessel"/ "Volume of water flowing per minute"`
`=(396000/21)/(33000/7)`
`=396/99`
= 4 minutes
Thus, the time required to fill the conical vessel is 4 minutes.
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