Find the rate of change of the area of a circle with respect to its radius $r$ when $r = 4$ cm

The correct answer is $8 \pi$ sq. cm

Consider $x$ denote the area of a circle with radius $r$

∴ $x = π r^2$
The rate of change of area $x$ with respect to radius $r$ is

$\dfrac{dx}{dr}$ = $2π r$

When $r=4$, $\dfrac{dx}{dr}$ = $2 π (4)$ = $8π$ sq. cm