The radius of a circle is increasing at the rate of 0.5 cm/sec. Find the rate of increase of its circumference.
Question:

The radius of a circle is increasing at the rate of 0.5 cm/sec. Find the rate of increase of its circumference.

Solution:

Let r be the radius and C be the circumference of the circle at any time t. Then,

$C=2 \pi r$

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

$\Rightarrow \frac{d C}{d t}=2 \pi \times 0.5$                 $\left[\because \frac{d r}{d t}=0.5 \mathrm{~cm} / \mathrm{sec}\right]$

$\Rightarrow \frac{d C}{d t}=\pi \mathrm{cm} / \mathrm{sec}$