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

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

• A. ³√[4(π)V / 3]
• B. V / 4(π)
• C. π / 3V
• D. ³√[3V / 4(π)]

Answer: (D)

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.

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.