The area of the circle is increasing at a uniform rate of $\displaystyle 2 \mathrm{~cm}^{2} / \mathrm{sec}$. How fast is the circumference of the circle increasing when the radius $\displaystyle \mathrm{r}=5 \mathrm{~cm}$ ?

Let $\displaystyle \mathrm{C}=2 \pi \mathrm{r}$, be the circumference of the circle,\frac{\mathrm{d}\left(\pi \mathrm{r}^{2}\right)}{\mathrm{dt}}=2 \Rightarrow \frac{\mathrm{dr}}{\mathrm{dt}}=\frac{1}{\pi \mathrm{r}} \mathrm{~cm} / \mathrm{sec}$\displaystyle \frac{\mathrm{dC}}{\mathrm{dt}}=2 \pi \frac{\mathrm{dr}}{\mathrm{dt}}=\frac{2}{\mathrm{r}}=\frac{2}{5} \mathrm{~cm} / \mathrm{sec}$ at $\displaystyle \mathrm{r}=5 \mathrm{~cm}$