Solve the following formula for [tex]$r$[/tex]:
[tex]
V=\frac{\pi r^2 h}{3}
[/tex]

A. [tex]r=\sqrt{\frac{3 V}{h^2 \pi}}[/tex]

B. [tex]r=\sqrt{\frac{h \pi}{3 V}}[/tex]

C. [tex]r=\sqrt{\frac{6 V}{h \pi}}[/tex]

D. [tex]r=\sqrt{\frac{3 V}{h \pi}}[/tex]



Answer :

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]