The volume of a sphere is increasing at the rate

(c) $1 / 36$

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

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

$\Rightarrow \frac{4}{3} \pi r^{3}=288 \pi$

$\Rightarrow r^{3}=\frac{288 \times 3}{4}$

$\Rightarrow r^{3}=216$

$\Rightarrow r=6$

$\Rightarrow \frac{d V}{d t}=4 \pi r^{2} \frac{d r}{d t}$

$\Rightarrow \frac{d V}{d t}=4 \pi(6)^{2} \frac{d r}{d t}$

$\Rightarrow 4 \pi=144 \pi \frac{d r}{d t}$

$\Rightarrow \frac{d r}{d t}=\frac{1}{36}$