Volume of a cube as a function of surface area

[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

[Mark44]

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
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}}


so we would have (SA/6^3)^3/2
No, you have too many factors of 6 in the denominator.



Is this correct answer to the question?
please help