35.6k views
5 votes
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) )

User Lars Bohl
by
8.4k points

1 Answer

5 votes

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).

User Flymike
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.