The radius of an air bubble is increasing at the rate of 0.5 cm/sec.

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

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

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

$\Rightarrow \frac{d V}{d t}=4 \pi(1)^{2} \times 0.5$     $\left(\because r=1 \mathrm{~cm}\right.$ and $\left.\frac{d r}{d t}=0.5 \mathrm{~cm} / \mathrm{sec}\right)$

$\Rightarrow \frac{d V}{d t}=2 \pi \mathrm{cm}^{3} / \mathrm{sec}$