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

  1. Sep 25, 2010 #1
    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


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

    Is this correct answer to the question?
    please help
  2. jcsd
  3. Sep 25, 2010 #2


    Staff: Mentor

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