Volume of a cube as a function of surface area

[lovemake1]

Homework Statement

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

Homework Equations

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

Homework Statement

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

Homework Equations

Surface area = 6x^2
Volume = x^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