What is the formula for finding r given the equation [4(π)r³ ] / 3 = V?

The correct choice is derived from rearranging the formula for the volume of a sphere, which is given by the equation [ V = \frac{4}{3} \pi r^3 ]. To isolate ( r ), we need to manipulate the equation step by step.

Starting with the original equation, we can first multiply both sides by (\frac{3}{4\pi}) to eliminate the fraction. This gives us:

[ r^3 = \frac{3V}{4\pi} ]

Now, to find ( r ), we take the cube root of both sides:

[ r = \sqrt[3]{\frac{3V}{4\pi}} ]

This matches the form of the option listed as the fourth choice.

In essence, this derivation emphasizes that to solve for ( r ), you must first rearrange the equation properly and then compute the cube root, leading directly to the correct relationship in the chosen answer.