Certainly! Let's solve the equation [tex]\( V = \frac{\pi r^2 h}{3} \)[/tex] for [tex]\( r \)[/tex]. We will follow a step-by-step approach to isolate [tex]\( r \)[/tex]:
1. Start with the given equation:
[tex]\[
V = \frac{\pi r^2 h}{3}
\][/tex]
2. Multiply both sides by 3 to clear the fraction:
[tex]\[
3V = \pi r^2 h
\][/tex]
3. Divide both sides by [tex]\( \pi h \)[/tex] to isolate [tex]\( r^2 \)[/tex]:
[tex]\[
\frac{3V}{\pi h} = r^2
\][/tex]
4. Take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[
r = \sqrt{\frac{3V}{\pi h}}
\][/tex]
After following these steps, we can see that the correct solution for [tex]\( r \)[/tex] is:
[tex]\[
r = \sqrt{\frac{3V}{\pi h}}
\][/tex]
Therefore, the correct answer is:
D. [tex]\( r = \sqrt{\frac{3V}{h \pi}} \)[/tex]
