Question

Find the rate of change of the area of a circle with respect to its radius r when r = 5 cm.

Answer 1

Let A be area of the circle. Then,
A = $\mathrm{\pi }{r}^2$

$\Rightarrow \frac{dA}{dr}=2\mathrm{\pi }r$
Hence, the rate of change of the area of the circle is $2\mathrm{\pi }r$.
When r = 5 cm,

$$\begin{gathered} {\left(\frac{dA}{dr}\right)}_{r=5}=2\mathrm{\pi }\left(5\right) \\ =10\mathrm{\pi }{\mathrm{cm}}^2/\mathrm{cm} \end{gathered}$$