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

$$\begin{gathered} \text{Let}\mathit{\text{r}}\text{be the radius and}\mathit{\text{C}}\text{be the circumference of the circle at any time}\mathit{\text{t.}}\text{Then,} \\ C=2\mathrm{\pi }r \\ \Rightarrow \frac{dC}{dt}=2\mathrm{\pi }\frac{dr}{dt} \\ \Rightarrow \frac{dC}{dt}=2\mathrm{\pi }\times 0.5\left[\text{∵}\frac{dr}{dt}\text{=0.5 cm/sec}\right] \\ \Rightarrow \frac{dC}{dt}=\mathrm{\pi }\mathrm{cm}/\sec \end{gathered}$$