Solving for a variable in an equation means, we are changing the subject of formula of the equation.
The equation of r is: [tex]\mathbf{r = \sqrt{\frac{3V}{\pi h}}}[/tex]
The equation is given as:
[tex]\mathbf{V = \frac 13 \pi r^2h}[/tex]
We start by multiplying both sides by 3
[tex]\mathbf{V \times 3= \frac 13 \pi r^2h \times 3}[/tex]
Rewrite as:
[tex]\mathbf{3V= \pi r^2h}[/tex]
Divide both sides by [tex]\mathbf{\pi h}[/tex]
[tex]\mathbf{\frac{3V}{\pi h}= \frac{\pi r^2h}{\pi h}}[/tex]
Cancel out common factors
[tex]\mathbf{\frac{3V}{\pi h}= r^2}[/tex]
Take square roots of both sides
[tex]\mathbf{\sqrt{\frac{3V}{\pi h}}= \sqrt{r^2}}[/tex]
Evaluate the right-hand sides
[tex]\mathbf{\sqrt{\frac{3V}{\pi h}}= r}[/tex]
Make r the subject
[tex]\mathbf{r = \sqrt{\frac{3V}{\pi h}}}[/tex]
Hence, the resulting equating for r is:
[tex]\mathbf{r = \sqrt{\frac{3V}{\pi h}}}[/tex]
Read more about the subject of formulas at:
https://brainly.com/question/21866313
