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Surface area to volume ratio problem

  1. Aug 30, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the surface area of a sphere whose volume is .2 m^3. For full credit, do it without finding the radius.

    2. Relevant equations
    This can be solved using
    v= 4/3(pi)r^3 and sa= 4(pi)r^2, but my prof doesn't want that.

    3. The attempt at a solution
    so if you manipulate the volume and surface area formulas you can get that the sa:v ratio is 3/r, by cancelling the variables and such. I don't know where to go from there, though, even after reading about the surface area to volume ratio. I did solve the problem using regular math (I got 1.7 m^2) but I haven't been able to do anything else useful without solving for r.

    Thanks in advance for any help.
  2. jcsd
  3. Aug 30, 2010 #2


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    Homework Helper

    You'll need to do something a little more complicated than just finding the ratio. You have two equations which share a common variable, r; try solving one of the equations for r and substituting it into the other one.
  4. Aug 30, 2010 #3
    Your problem does not require finding "surface to volume ratio". It simply asks you what the surface area of a sphere with a known volume is.


    What is the ratio:

    \frac{SA^{3}}{V^2} = ?

    equal to? Is it dependent on the radius? Can you solve this equation with respect to V?
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