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.

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is B

If V be the volume of liquid in the cylinder, at a height h of the water level, then $V=\pi r^{2}h$
Differentiating both sides w.r.t time t, we get
$\frac{dV}{dt}=\pi r^2\frac{dh}{dt}\Rightarrow Q=\pi r^2\frac{dh}{dt}or\Rightarrow \frac{dh}{dt}=\frac{Q}{\pi r^2}$
Note that $\frac{dV}{dt}$ 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.