The figure to the right shows an open box with a square base.

Question

The figure to the right shows an open box with a square base. The box is to have a volume of 7 cubic feet. Express the amount of material needed to construct the​ box, A, as a function of the length of a side of its square​ base, x.

The Image is A rectangular prism with y as the height, and x on both width and length

Answer 1

Th side of the square base is x and the height of the box is y.

The volume 7 = x²y

The surface are of the open box (which is the amount of material needed) is

(x+y)² - 4y²

Draw a figure with the box flattened out to see why this is so

Now substitute y=7/(x²) to get the amount of material as a function of x alone.