An open box with a square base is to have a volume of 8 ft3. Find a function that models the surface area A of the box in terms of the length of one side of the base x.

Answer 1

Let x = length of a side of the base and y = height.

Then, x²y = 8, so y = 8 / x².

Surface area = 2x² + 4xy (assuming that the box has a top)

So A = 2x² + 4x(8/x²) = 2x² + 32/x