Water pours out rate of Q from a tap, into a cylindrical vessel of radius r. The rate at which the height of water level rises the height is h, is

Explanation

If V be the volume of liquid in the cylinder, at a height h of the water level, then `V=pir^2h`.
Differentiating both sides w.r.t time t, we get
`(dV)/(dt)=pir^2(dh)/(dt)`
`impliesQ=pir^2(dh)/(dt)` or `(dh)/(dt)=(Q)/(pir^2)`
Note that `dV//dt` represents the rate at which the volume of liquid in the cylinder increases, which is same as the rate of pouring of water through the tap.