Question

solve the equation $x = \frac{4}{3}\pi r^3$ for $r$.
\bigcirc a. $r = \sqrt3{3x - 4\pi}$
\bigcirc b. $r = \sqrt3{\frac{3x}{4\pi}}$
\bigcirc c. $r = \sqrt3{3x(4\pi)}$
\bigcirc d. $r = \sqrt3{\frac{4\pi}{3x}}$

Explanation:

Step1: Isolate the $r^3$ term

Multiply both sides by $\frac{3}{4\pi}$:
$\frac{3x}{4\pi} = r^3$

Step2: Solve for $r$

Take cube root of both sides:
$r = \sqrt[3]{\frac{3x}{4\pi}}$

Answer:

B. $r = \sqrt[3]{\frac{3x}{4\pi}}$