Question

Water pours out at the rate of Q from a tap, into a cylindrical vessel of radius r. Find the rate at which the height of water level rises when the height is h.
[Kindly solve by calculus]

Answer 1

Answer:

Explanation: :

If V be the volume of liquid in the cylinder, at a height h of the water level, then V=πr2h.

Differentiating both sides w.r.t time t, we get

dVdt=πr2dhdt

⇒Q=πr2dhdt or dhdt=Qπr2

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.