The rate of change of the area of a circle with respect to its radius r at r = 6 cm is

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

$A=\pi r^{2}$

Therefore, the rate of change of the area with respect to its radius r is

$\frac{d A}{d r}=\frac{d}{d r}\left(\pi r^{2}\right)=2 \pi r$

$\therefore$ When $r=6 \mathrm{~cm}$,

Hence, the required rate of change of the area of a circle is $12 \pi \mathrm{cm}^{2} / \mathrm{s}$.

The correct answer is B.