Surface area to volume ratio problem

[uchicago2012]

Homework Statement

Find the surface area of a sphere whose volume is .2 m^3. For full credit, do it without finding the radius.

Homework 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.

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.

 

[diazona]

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.

 

[Dickfore]

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.

Hint:

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?