Solve 22176=pir^2

$$22176 = \pi r ^ { 2 }$$

Solve for r

$$r=12\sqrt{\frac{154}{\pi }}\approx 84.016903276$$

$$r=-12\sqrt{\frac{154}{\pi }}\approx -84.016903276$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$\pi r^{2}=22176$$

Divide both sides by \pi .

$$\frac{\pi r^{2}}{\pi }=\frac{22176}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$r^{2}=\frac{22176}{\pi }$$

Take the square root of both sides of the equation.

$$r=\frac{1848}{\sqrt{154\pi }} r=-\frac{1848}{\sqrt{154\pi }}$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$\pi r^{2}=22176$$

Subtract 22176 from both sides.

$$\pi r^{2}-22176=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -22176 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\pi \left(-22176\right)}}{2\pi }$$

Square 0.

$$r=\frac{0±\sqrt{-4\pi \left(-22176\right)}}{2\pi }$$

Multiply -4 times \pi .

$$r=\frac{0±\sqrt{\left(-4\pi \right)\left(-22176\right)}}{2\pi }$$

Multiply -4\pi times -22176.

$$r=\frac{0±\sqrt{88704\pi }}{2\pi }$$

Take the square root of 88704\pi .

$$r=\frac{0±24\sqrt{154\pi }}{2\pi }$$

Now solve the equation r=\frac{0±24\sqrt{154\pi }}{2\pi } when ± is plus.

$$r=\frac{1848}{\sqrt{154\pi }}$$

Now solve the equation r=\frac{0±24\sqrt{154\pi }}{2\pi } when ± is minus.

$$r=-\frac{1848}{\sqrt{154\pi }}$$

The equation is now solved.

$$r=\frac{1848}{\sqrt{154\pi }} r=-\frac{1848}{\sqrt{154\pi }}$$