Find the dimensions of a rectangular box of maximum volume if the total surface area is given as 64cm^2.
Let the base be m and height be n. I am assuming the problem indicates square base is used.
Assuming the box has an open top, the surface area is
Solve for n from the surface area, then plug the expressions into the volume formula.
Find the first derivative of volume:
Then solve for m.
The story changes if this is a closed top box.