Solve pir^2=13.86

$$\pi r ^ { 2 } = 13.86$$

Solve for r

$$r = \frac{3 \sqrt{\frac{154}{\pi}}}{10} \approx 2.100422582$$

$$r = -\frac{3 \sqrt{\frac{154}{\pi}}}{10} \approx -2.100422582$$

Steps by Finding Square Root

Divide both sides by \pi .

$$\frac{\pi r^{2}}{\pi }=\frac{13.86}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$r^{2}=\frac{13.86}{\pi }$$

Divide 13.86 by \pi .

$$r^{2}=\frac{693}{50\pi }$$

Take the square root of both sides of the equation.

$$r=\frac{231}{5\sqrt{154\pi }} r=-\frac{231}{5\sqrt{154\pi }}$$

Steps Using the Quadratic Formula

Subtract 13.86 from both sides.

$$\pi r^{2}-13.86=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -13.86 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\pi \left(-13.86\right)}}{2\pi }$$

Square 0.

$$r=\frac{0±\sqrt{-4\pi \left(-13.86\right)}}{2\pi }$$

Multiply -4 times \pi .

$$r=\frac{0±\sqrt{\left(-4\pi \right)\left(-13.86\right)}}{2\pi }$$

Multiply -4\pi times -13.86.

$$r=\frac{0±\sqrt{\frac{1386\pi }{25}}}{2\pi }$$

Take the square root of \frac{1386\pi }{25}.

$$r=\frac{0±\frac{3\sqrt{154\pi }}{5}}{2\pi }$$

Now solve the equation r=\frac{0±\frac{3\sqrt{154\pi }}{5}}{2\pi } when ± is plus.

$$r=\frac{231}{5\sqrt{154\pi }}$$

Now solve the equation r=\frac{0±\frac{3\sqrt{154\pi }}{5}}{2\pi } when ± is minus.

$$r=-\frac{231}{5\sqrt{154\pi }}$$

The equation is now solved.

$$r=\frac{231}{5\sqrt{154\pi }} r=-\frac{231}{5\sqrt{154\pi }}$$