Applied Maximum and Minimum

Question

A closed box, whose length is thrice its width, is to have a surface of 200 square cm. Find the maximum Volume of the box? 

Answer 1

Maximum volume for a rectangular box is with a cube, where each side S is equal. height = length = width = H=L=W = S

surface area = 200 = 2(H+L+W) = 2(S+S+S) = 6S or 100 = 3S and S= 100/3 = 33 1/3 cm

Maximum volume = S^3 = (100/3)^3 = 1000000/27 = 37,373 7/27 cubic centimeters