Question

solve $v = \frac{1}{3}pi r^{2}h$ for $r$

Explanation:

Step1: Isolate $r^{2}$ term

Multiply both sides by 3 to get $3V=\pi r^{2}h$. Then divide both sides by $\pi h$, so $r^{2}=\frac{3V}{\pi h}$.

Step2: Solve for $r$

Take the square - root of both sides. Since $r$ represents a radius (usually non - negative in geometric contexts), $r = \sqrt{\frac{3V}{\pi h}}$ (we consider the positive square root as radius is a non - negative quantity in most practical scenarios).

Answer:

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