Question

A rectangular box with a square base is open at the top and has a volume of 12 cubic feet. Each side of the base has a length of x feet. Which of the following expresses the surface area, S, in square feet, of the outside of the box in terms of x?

a) $S=5x^{2}$
b) $S= \frac{12}{ x^{2} }$
c) $S= x^{2} + \frac{24}{x}$
d) $S= x^{2} + \frac{48}{x}$
e)$S= x^{2} + \frac{48}{ x^{2} }$

Answer 1

We know that the side lengths of the square base are: x * x. The volume is 12, so for now, let's say that y is the other side length. Then, x * x * y = 12. We can solve for y: y = 12/x^2. Now, we find the surface area of the 5 sides.

Four of the sides have the same area: x * (12/x^2) = 12/x, so we multiply this by 4: 48/x.

The last side is the base: x * x = x^2.

We add 48/x to x^2:

x^2 + 48/x

So, the answer is the fourth choice, (d).