To solve the formula [tex]\( V = \frac{1}{6} \pi r^3 \)[/tex] for [tex]\( r \)[/tex], we can follow these steps:
1. Isolate [tex]\( r \)[/tex] in the formula:
Start with the volume formula:
[tex]\[
V = \frac{1}{6} \pi r^3
\][/tex]
2. Eliminate the fraction:
Multiply both sides of the equation by 6 to get rid of the fraction:
[tex]\[
6V = \pi r^3
\][/tex]
3. Isolate [tex]\( r^3 \)[/tex]:
Divide both sides by [tex]\( \pi \)[/tex] to solve for [tex]\( r^3 \)[/tex]:
[tex]\[
r^3 = \frac{6V}{\pi}
\][/tex]
4. Solve for [tex]\( r \)[/tex]:
Take the cube root of both sides to isolate [tex]\( r \)[/tex]:
[tex]\[
r = \sqrt[3]{\frac{6V}{\pi}}
\][/tex]
Thus, the correct answer is:
A. [tex]\( r = \sqrt[3]{\frac{6 V}{\pi}} \)[/tex]
