To solve the formula [tex]\( V = \pi r^2 h \)[/tex] for [tex]\( r \)[/tex], follow these detailed steps:
1. Start with the given formula:
[tex]\[
V = \pi r^2 h
\][/tex]
2. Isolate the term involving [tex]\( r \)[/tex]:
[tex]\[
V = \pi r^2 h
\][/tex]
3. Divide both sides by [tex]\( \pi h \)[/tex] to isolate [tex]\( r^2 \)[/tex]:
[tex]\[
\frac{V}{\pi h} = r^2
\][/tex]
4. Take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[
r = \pm \sqrt{\frac{V}{\pi h}}
\][/tex]
Since [tex]\( r \)[/tex] (radius) is a geometric measurement, we typically consider only the positive value in this context unless otherwise specified.
5. Thus, the solution for [tex]\( r \)[/tex] is:
[tex]\[
r = \sqrt{\frac{V}{\pi h}}
\][/tex]
Therefore, the correct answer is:
C. [tex]\( r = \sqrt{\frac{V}{\pi h}} \)[/tex]
