Solve $$ g=\sqrt[3]{\frac{8 S}{9 \pi}} $$ for S $$ S=\square $$ (Simplify your answer.)

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Solve the equation $$ g=\sqrt[3]{\frac{8 S}{9 \pi}} $$.
Solve the equation by following steps:
- step0: Solve for $$S$$:
  $$g=\sqrt[3]{\frac{8S}{9\pi }}$$
- step1: Use the properties of radicals:
  $$g=\frac{\sqrt[3]{8S}}{\sqrt[3]{9\pi }}$$
- step2: Swap the sides:
  $$\frac{\sqrt[3]{8S}}{\sqrt[3]{9\pi }}=g$$
- step3: Cross multiply:
  $$\sqrt[3]{8S}=\sqrt[3]{9\pi }	imes g$$
- step4: Simplify the equation:
  $$\sqrt[3]{8S}=g\sqrt[3]{9\pi }$$
- step5: Simplify the equation:
  $$\left(\sqrt[3]{8S}ight)^{3}=\left(g\sqrt[3]{9\pi }ight)^{3}$$
- step6: Evaluate:
  $$8S=9\pi g^{3}$$
- step7: Divide both sides:
  $$\frac{8S}{8}=\frac{9\pi g^{3}}{8}$$
- step8: Divide the numbers:
  $$S=\frac{9\pi g^{3}}{8}$$
The solution to the equation $$ g=\sqrt[3]{\frac{8 S}{9 \pi}} $$ for S is $$ S=\frac{9\pi g^{3}}{8} $$.
$$ S = \frac{9\pi g^{3}}{8} $$

Solve \( g=\sqrt[3]{\frac{8 S}{9 \pi}} \) for S \( S=\square \) (Simplify your answer.)

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