Step 1

Surface area of sphere is \(\displaystyle{S}={4}\pi{r}^{{{2}}}\).

And rate of change means derivatives.

Step 2

Now let radius of sphere is =r.

So dr/dt=4.

So rate of change of surface area \(\displaystyle={d}\frac{{S}}{{\left.{d}{t}\right.}}={8}\pi{r}.{}\frac{{dr}}{{\left.{d}{t}\right.}}={8}\pi{.9}{.4}={288}\pi\).

So options A correct.