Surface area S of the box as a function?

Question

An open rectangular box (no top) with volume 4 cubic meters has a square base. Express the surface area of the box as a function of the length of one of the sides of the base.

Answer 1

Let X be base length.

First, find our the height of the box (Volume=area of the base * h):

4 = x^2 * h

So h=4/x^2

Now, the surface area is base + 4 sides:

x^2 + 4*x*h

Substituting h from the above:

x^2 + 4*x*4/x^2

Or, simplifying a bit

x^2 + 16/x