Step 1

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

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 \(= dS/dt= 8\pi r.dr/dt =8\pi .9.4=288\pi\).

So options A correct.

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

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 \(= dS/dt= 8\pi r.dr/dt =8\pi .9.4=288\pi\).

So options A correct.