A circular disc of radius 3 cm is being heated. Due to expansion,
Question:

A circular disc of radius 3 cm is being heated. Due to expansion, its radius increases at the rate of 0.05 cm/sec. Find the rate at which its area is increasing when radius is 3.2 cm.

Solution:

Let $r$ be the radius and $A$ be the area of the circular disc at any time $t .$ Then,

$A=\pi r^{2}$

$\Rightarrow \frac{d A}{d t}=2 \pi r \frac{d r}{d t}$

$\Rightarrow \frac{d A}{d t}=2 \pi \times 3.2 \times 0.05$    $\left[\because r=3.2 \mathrm{~cm}\right.$ and $\left.\frac{d r}{d t}=0.05 \mathrm{~cm} / \mathrm{sec}\right]$

$\Rightarrow \frac{d A}{d t}=0.32 \pi \mathrm{cm}^{2} / \mathrm{sec}$