Problem 1027

Solve the following equation for r.

F = $\frac{1}{3}\pi r^{2}h$

Solution:-

First rewrite the equation with the expression containing r on the left side .

$\frac{1}{3}\pi r^{2}h$ = F

To rewrite the formula with only the r on the left side, multiply by 3, then simplify.

3* $\frac{1}{3}\pi r^{2}h$ = F*3

Divide both sides by πh to isolate the expression containing r on the left side.

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

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

Use the square root property to solve for r.

r= ± $\sqrt{\frac{3F}{\pi h}}$