Chapter 6 Rational Exponents and Radical Functions - Standardized Test Practice - Extended Response - Page 472: 4b

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From part a, $r=\sqrt \frac{S}{3\pi}$ The volume formula: $V=\frac{2}{3}\pi r^3\\=\frac{2}{3}\pi(\sqrt \frac{S}{3\pi})^3\\=\frac{2}{3}\pi( \frac{S}{3\pi})^{3/2}\\=\frac{2\pi^{-1/2}}{3^{5/2}}S^{3/2}\\=\frac{2}{3^{5/2}\pi^{1/2}}S^{3/2}$