Find the rate of change of the area of a circle with respect to its radius r when

The area of a circle (A)with radius (r) is given by,

$A=\pi r^{2}$

Now, the rate of change of the area with respect to its radius is given by, $\frac{d A}{d r}=\frac{d}{d r}\left(\pi r^{2}\right)=2 \pi r$

1. When $r=3 \mathrm{~cm}$,

$\frac{d A}{d r}=2 \pi(3)=6 \pi$

Hence, the area of the circle is changing at the rate of 6π cm when its radius is 3 cm.

2. When $r=4 \mathrm{~cm}$,

$\frac{d A}{d r}=2 \pi(4)=8 \pi$

Hence, the area of the circle is changing at the rate of 8π cm when its radius is 4 cm.