Solve piR^2=18

$$\pi R ^ { 2 } = 18$$

Solve for R

$$R=3\sqrt{\frac{2}{\pi }}\approx 2.393653682$$

$$R=-3\sqrt{\frac{2}{\pi }}\approx -2.393653682$$

Steps by Finding Square Root

Divide both sides by \pi .

$$\frac{\pi R^{2}}{\pi }=\frac{18}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$R^{2}=\frac{18}{\pi }$$

Take the square root of both sides of the equation.

$$R=\frac{6}{\sqrt{2\pi }} R=-\frac{6}{\sqrt{2\pi }}$$

Steps Using the Quadratic Formula

Subtract 18 from both sides.

$$\pi R^{2}-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R=\frac{0±\sqrt{0^{2}-4\pi \left(-18\right)}}{2\pi }$$

Square 0.

$$R=\frac{0±\sqrt{-4\pi \left(-18\right)}}{2\pi }$$

Multiply -4 times \pi .

$$R=\frac{0±\sqrt{\left(-4\pi \right)\left(-18\right)}}{2\pi }$$

Multiply -4\pi times -18.

$$R=\frac{0±\sqrt{72\pi }}{2\pi }$$

Take the square root of 72\pi .

$$R=\frac{0±6\sqrt{2\pi }}{2\pi }$$

Now solve the equation R=\frac{0±6\sqrt{2\pi }}{2\pi } when ± is plus.

$$R=\frac{6}{\sqrt{2\pi }}$$

Now solve the equation R=\frac{0±6\sqrt{2\pi }}{2\pi } when ± is minus.

$$R=-\frac{6}{\sqrt{2\pi }}$$

The equation is now solved.

$$R=\frac{6}{\sqrt{2\pi }} R=-\frac{6}{\sqrt{2\pi }}$$