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Question
Water is being poured at the rate of 36 m3/sec in to a cylindrical vessel of base radius 3 meters. Find the rate at which water level is rising
Solution
Let h be the height of water level, r be the radius of the base and V be the volume of the cylindrical vessel.
Then, r = 3 metres, `("dV")/("dT")`
= 36 m3/sec
V = πr2h
= π(3)2h
= 9πh
Differentiating w.r.t.t, we get
`("dV")/("dt") = 9pi*("dh")/("dt")`
∴ `("dh")/("dt") = (("dV")/("dt")) xx 1/(9pi)`
= `36/(9pi)`
= `4/pi` m/sec
Thus, water level is rising at the rate of `4/pi` m/sec.
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