Question

Find the surface S of the balloon as a function of the time t.

Answer 1

seems to be just a matter of  S( r(t) )

$\bf \textit{surface area of a sphere}\\\\ S=4\pi r^2\qquad \begin{cases} r=radius\\ --------\\ \boxed{r(t)}=\frac{3}{8}t^4 \end{cases}\implies S(t)=4\pi \left( \boxed{\frac{3}{8}t^4} \right)^2$