# How do you solve for r in V=πr^2h?

Feb 10, 2017

$r = \sqrt{\frac{V}{\pi h}}$

#### Explanation:

Step 1. Divide both sides by $\pi$

$\frac{V}{\pi} = \frac{\cancel{\pi} {r}^{2} h}{\cancel{\pi}} = {r}^{2} h$

Step 2. Divide both sides by $h$

$\frac{V}{\pi h} = \frac{{r}^{2} \cancel{h}}{\cancel{h}} = {r}^{2}$

Step 3. Take $\pm \sqrt{}$ both sides

$\pm \sqrt{\frac{V}{\pi h}} = r$

Step 4. Radius, $r$, is not a negative value, so just keep the positive

$r = \sqrt{\frac{V}{\pi h}}$