# Homework Help: Volume of a cube as a function of surface area

1. Sep 25, 2010

### lovemake1

1. The problem statement, all variables and given/known data

Express the volume of a cube as a fuction of the total surface area

2. Relevant equations

Surface area = 6x^2
Volume = x^3

3. The attempt at a solution

So, we need to manipulate the surface area equation so we can use it to find volume right?

SA = 6x^2
sqrt(SA/6) = x
or (SA/6)^(1/2) = x

and sub it in the Volume equation

(SA/6)^(1/2)*3

so we would have (SA/6^3)^3/2

Is this correct answer to the question?
please help

2. Sep 25, 2010

### Staff: Mentor

You should actually have an equation. Let's call S the surface area.
V = x3 = (S/6)3/2
or
$$V = (\frac{S}{6})^{3/2}$$
You can also write this as $$\frac{S^{3/2}}{6^{3/2}} = \frac{S^{3/2}}{6\sqrt{6}}$$
No, you have too many factors of 6 in the denominator.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook