To solve the equation [tex]\( V = \pi r^2 h \)[/tex] for [tex]\( r \)[/tex], let's go through the steps methodically:
1. Start with the original formula:
[tex]\[ V = \pi r^2 h \][/tex]
2. Isolate [tex]\( r^2 \)[/tex] by dividing both sides by [tex]\( \pi h \)[/tex]:
[tex]\[ \frac{V}{\pi h} = r^2 \][/tex]
3. Solve for [tex]\( r \)[/tex] by taking the square root of both sides:
[tex]\[ r = \sqrt{\frac{V}{\pi h}} \][/tex]
Based on the above steps, the correct equation that isolates [tex]\( r \)[/tex] is:
[tex]\[ r = \sqrt{\frac{V}{\pi h}} \][/tex]
Now, let's compare this result to the given choices:
A. [tex]\( r = \sqrt{\frac{V}{\pi h}} \)[/tex]
B. [tex]\( r = \sqrt{\frac{V}{\pi} - h} \)[/tex]
C. [tex]\( r = \frac{V_{\pi h}}{2} \)[/tex]
D. [tex]\( r = \frac{V}{2 \pi h} \)[/tex]
The correct answer is:
[tex]\[ \boxed{A} \][/tex]
