$V = \frac{A}{3} \sqrt{\frac{A}{4\pi}}$

$V = \frac{2}{3} A \sqrt{A}$

$V = \frac{4}{3} \pi (\frac{A}{4\pi})^{3/2}$

$V = \frac{1}{6} \sqrt{\frac{A^3}{\pi}}$