Question

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

• A. $\frac{Q}{\pi rh}$
• B. $\frac{Q}{\pi r^2}$
• C. $\frac{Q}{2\pi r^2}$
• D. $\frac{Q}{\pi r^{2}h}$

Answer 1

The correct option is B $\frac{Q}{\pi r^2}$

Volume of cylindrical vessel when height is h
$V=\pi r^{2}h$
Rate of change of volume of water w.r.t. to t in vessel is $\frac{dV}{dt}=\pi r^2\frac{dh}{dt}$
And we know water pours in the vessel at the rate of Q
Hence, $\frac{dV}{dt}=Q$
So, $\frac{dh}{dt}=\frac{Q}{\pi r^2}$