1. ## Simplify?

Is it possible to simplify (2pi^3)/3 - (2pir^3)/(3sqrt.3)
the furthest I was able to go was (2sqrt.3 r^3 - 2pi r^3) / (3sqrt.3)

2. $\displaystyle \frac{2\pi^{3} }{3} \cdot {\color{blue} \frac{\sqrt{3}}{\sqrt{3}}} \:\: - \:\: \frac{2\pi r^{3}}{3 \sqrt{3}} = \frac{2\pi^{3} \sqrt{3} - 2\pi r^{3}}{3\sqrt{3}}$

Not much else you can do ... unless you factor a bit but that doesn't do a whole lot:
$\displaystyle \frac{2\pi \left(\pi^{2} \sqrt{3} - r^{3}\right)}{3\sqrt{3}}$

3. What if you were to rationalize the denominator?

4. Sure:
$\displaystyle \frac{2\pi^{3} \sqrt{3} - 2\pi r^{3}}{3\sqrt{3}} \cdot {\color{blue}\frac{\sqrt{3}}{\sqrt{3}}}$

$\displaystyle = \frac{6\pi^{3} - 2\pi r^{3} \sqrt{3}}{{\color{red}9}}$

Doesn't change it too much. I don't think it matters too much at this point how the expression is represented.

Edited.

5. Originally Posted by o_O
Sure:
$\displaystyle \frac{2\pi^{3} \sqrt{3} - 2\pi r^{3}}{3\sqrt{3}} \cdot {\color{blue}\frac{\sqrt{3}}{\sqrt{3}}}$

$\displaystyle = \frac{6\pi^{3} - 2\pi r^{3} \sqrt{3}}{3}$

Doesn't change it too much. I don't think it matters too much at this point how the expression is represented.
Wouldn't it be 9 in the denominator?

6. Yes, just a typo. Nonetheless, it really doesn't matter what it is represented as at this point.