The rate of change of the area of a circle with respect to its radius $r$, when $r = 3\,cm$, is:

$6π\, cm^2/cm$

The correct answer is Option (1) → $6π\, cm^2/cm$

$\text{Area of circle }A=\pi r^2.$

$\frac{dA}{dr}=\frac{d}{dr}(\pi r^2).$

$\frac{dA}{dr}=2\pi r.$

$r=3.$

$\frac{dA}{dr}=2\pi(3).$

$\frac{dA}{dr}=6\pi.$

$\text{Rate of change of area}=6\pi\ \text{cm}.$