Question

Water is being poured at the rate of $36m^3/sec$ in a cylindrical vessel of base radius $3$ meters. Find the rate at which water level is rising.

Answer 1

Volume of cylinder,

$V=\pi r^{2}h$

differentiating on both sides,

$\frac{dV}{dt}=\pi r^2\frac{dh}{dt}$

$36=\pi \times 3^2\times \frac{dh}{dt}$

$\frac{dh}{dt}=\frac{36}{9\pi }=\frac{4}{\pi }$

height of water level increasing at a rate of $\frac{4}{\pi }$