The radius of a cylinder is increasing at the rate 2cm/sec. and its altitude is decreasing at the rate of 3cm/sec. Find the rate of change of volume when radius is 3 cm and altitude 5 cm.

Explanation

`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(2 h frac{d r}{d t}+r frac{d h}{d t})`


`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 {cm}^{3} / {sec}`