Arectangular solid (with a square base has a surface area of 37.5 square centimeters. find the dimensions that will result in a solid with maximum volume.

The total surface area of the solid is equal to 37.5 which is

37.5 = 2s^2 + 4sh
h = 37.5 - s^2 / 4s

The volume of the solid is expressed in

V=s^2h
V= s^2 (37.5 - s^2 / 4s)
V' = 9.735 - 3s^2/4 = 0

s= 3.5355
h = 1.7678

Ithink billy is a good guy