Question
Solve \( g=\sqrt[3]{\frac{8 S}{9 \pi}} \) for S \( S=\square \) (Simplify your answer.)
Ask by Fuentes Sherman. in the United States
Mar 14,2025
Upstudy AI Solution
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Answer
\( S = \frac{9\pi g^{3}}{8} \)
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The Deep Dive
To solve for \( S \) in the equation \( g = \sqrt[3]{\frac{8 S}{9 \pi}} \), we first cube both sides to eliminate the cube root: \[ g^3 = \frac{8 S}{9 \pi} \] Next, we solve for \( S \) by multiplying both sides by \( 9 \pi \): \[ 9 \pi g^3 = 8 S \] Now, we divide both sides by 8: \[ S = \frac{9 \pi g^3}{8} \] Thus, the simplified answer is: \( S = \frac{9 \pi g^3}{8} \)