The volume of a sphere of radius r is V = (4/3)(pi)(r^3); the surface area S of this sphere is S = 4(pi)(r^2).
(a) Express the volume V as a function of the surface area S.
(b) If the surface area doubles, how does the volume change?
Now, we need to take the square root of both sides. It was more convenient for me to express this as
rather than
Both of these forms are completely equivalent, though you would probably recognize the second as being more familiar. Perhaps I should have mentioned this when I solved the problem.
-Dan