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= (12)/( x^(2) )`
c) 
`S= x^(2) + (24)/(x)`
d) 
`S= x^(2) + (48)/(x)`
e)
`S= x^(2) + (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).