Question

The radius of a sphere is increasing at a constant rate of 2cm/sec. At the instant when the volume of the sphere is 36π cm^3, what is the rate that the surface area is increasing? Surface area=4π r^2 Volume=4/3π r^3

Answer 1

\[S(r(t))=4\pi r^2\]
\[S'(r(t))=8\pi r r'\] and you are told that
\[r'=2\] so this becomes
\[S'(r(t))=16\pi r\] now your only job is to find r and substitute

Answer 2

How do I find r?