At what approximate rate (in cubic meters per minute) is the volume of a sphere changing at the instant when the surface area is 4 square meters and the radius is increasing at the rate of 1/6 meters per minute?
We know the volume of a sphere relative to its radius is given by:
We are given that
Surface area at the time in question is
which implies since
We are asked for
and we are told that
So at the time indicated