To find the radius [tex]\( r \)[/tex] when the volume of each wedge is given by [tex]\( V = \frac{2}{9} \pi r^3 \)[/tex], we need to isolate [tex]\( r \)[/tex] in this equation. Let's solve it step-by-step:
1. Start with the given formula for the volume of each wedge:
[tex]\[
V = \frac{2}{9} \pi r^3
\][/tex]
2. Rearrange the equation to solve for [tex]\( r^3 \)[/tex]. To do this, multiply both sides of the equation by [tex]\(\frac{9}{2\pi}\)[/tex] to isolate [tex]\( r^3 \)[/tex] on one side:
[tex]\[
r^3 = \frac{9V}{2\pi}
\][/tex]
3. Take the cube root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[
r = \sqrt[3]{\frac{9V}{2\pi}}
\][/tex]
Therefore, the correct answer is:
A. [tex]\( r = \sqrt[3]{\frac{9V}{2\pi}} \)[/tex]
