In a sphere the rate of change of volume is

(c) surface area times the rate of change of radius

Let r be the radius and V be the volume of sphere at any time t. Then,

$V=\frac{4}{3} \pi r^{3}$

$\Rightarrow \frac{d V}{d t}=\frac{4}{3}\left(3 \pi r^{2}\right)\left(\frac{d r}{d t}\right)$

$\Rightarrow \frac{d V}{d t}=4 \pi r^{2}\left(\frac{d r}{d t}\right)$

Thus, the rate of change of volume is surface area times the rate of change of the radius.