The radius of a cylinder is increasing at the rate 2 cm/sec.

Let $r$ be the radius, $h$ be the height and $V$ be the volume of the cylinder at any time $t .$ Then,

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

$\Rightarrow \frac{d V}{d t}=2 \pi r h \frac{d r}{d t}+\pi r^{2} \frac{d h}{d t}$

$\Rightarrow \frac{d V}{d t}=\pi r\left(2 h \frac{d r}{d t}+r \frac{d h}{d t}\right)$

$\Rightarrow \frac{d V}{d t}=\pi \times 3(2 \times 5 \times 2+3 \times-3)$

$\Rightarrow \frac{d V}{d t}=3 \pi(20-9)$

$\Rightarrow \frac{d V}{d t}=33 \pi \mathrm{cm}^{3} / \mathrm{sec}$