Consider the problem of cutting corners out of a rectangle and folding up the sides to make a box.
(a) In the solution to Example 3, compare the area of the base of the box with the area of the walls.
(b) Repeat part (a) for the solution to Exercise 25.
(c) Make a conjecture about the area of the base compared with the area of the walls for the box with the maximum volume.

Example 3

A supplier of bolts wants to create open boxes for the bolts by cutting a square from each corner of a 12-in. by 12-in. piece of metal and then folding up the sides. What size square should be cut from each corner to produce a box of maximum volume?