#### Answer

a) $r=2t$
b) $V(r(t))=\frac{32}{3}\pi t^{3},$ the volume of the balloon as a function of time.

#### Work Step by Step

a) Rate of increase of radius$=\frac{r}{t}=2$
$r=2t$
b) $V(r(t))=\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi (2t)^{3}=\frac{32}{3}\pi t^{3}$
This is the volume of the balloon as a function of time.