Question

A box with an open top is to be constructed by cutting a-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 32 in^3, when a = 2?
width in
length in

Answer 1

If the original
width is x
length is 2x

With a=2, our new box has volume

(a)(x-2a)(2x-2a) = 32
2(x-4)(2x-4) = 32
2(x-4)(2x-4) - 32 = 0
4x(x-6) = 0
x = 6

So a sheet 6x12 will be cut to a box
2x2x8 with volume = 32