To solve the given formula for [tex]\( r \)[/tex], we start with the equation:
[tex]\[ V = \pi r^2 h \][/tex]
We want to isolate [tex]\( r \)[/tex], so let's perform the algebraic steps step-by-step.
1. Divide both sides by [tex]\(\pi h\)[/tex]:
[tex]\[
\frac{V}{\pi h} = r^2
\][/tex]
2. Take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[
r = \sqrt{\frac{V}{\pi h}}
\][/tex]
Now, let's compare this result with the given options:
A. [tex]\[
r = \sqrt{\frac{V}{\pi h}}
\][/tex]
This matches our derived equation.
B. [tex]\[
r = \sqrt{\frac{V}{\pi} - h}
\][/tex]
This is not correct because it incorrectly subtracts [tex]\( h \)[/tex] instead of representing the division and then the square root.
C. [tex]\[
r = \frac{V \pi h}{2}
\][/tex]
This is incorrect because it has an entirely misplaced formula involving multiplication and different positioning of terms.
D. [tex]\[
r = \frac{V}{2 \pi h}
\][/tex]
This is incorrect as it suggests simple division without the square root, and the denominator differs from our derived formula.
Therefore, the correct answer is:
[tex]\[
\boxed{r = \sqrt{\frac{V}{\pi h}}}
\][/tex]
Thus, the correct option is:
A. [tex]\( r = \sqrt{\frac{V}{\pi h}} \)[/tex]
