Question

solve the formula for the indicated variable.
volume of a cone with radius $r$.
$v = \frac{1}{3}\pi r^{2}h$; solve for $r$

Explanation:

Step1: Isolate $r^2$ term

Multiply both sides by 3:
$$3V = \pi r^2 h$$

Step2: Divide by $\pi h$

$$\frac{3V}{\pi h} = r^2$$

Step3: Take square root

$$r = \sqrt{\frac{3V}{\pi h}}$$
(We take positive root as radius is positive)

Answer:

$r = \sqrt{\frac{3V}{\pi h}}$