What is the volume of a box that can be created from a sheet of metal that measures 12 inches by 30 inches? Assume there is no top to the box.

Answer 1

If this is the typical question where equal sized squares are cut out at each corner, the volume will depend on the size of the cut-out squares

Suppose we cut out a square on each corner of x inches by x inches
then length of base = 30-2x
width of base = 12-2x
height = x

volume = x(30-2x)(12-2x) , where clearly 0<x<6

Perhaps, did the question ask for the maximum volume ?

Answer 2

I assume that square corners are cut and the sides are folded up, so that the sides are all the same height, call it z.

v = (12-2z)(30-2z)(z)