Solve piR^2=35.8

$$\pi R ^ { 2 } = 35.8$$

Solve for R

$$R = \frac{\sqrt{\frac{895}{\pi}}}{5} \approx 3.375721245$$

$$R = -\frac{\sqrt{\frac{895}{\pi}}}{5} \approx -3.375721245$$

Steps by Finding Square Root

Divide both sides by \pi .

$$\frac{\pi R^{2}}{\pi }=\frac{35.8}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$R^{2}=\frac{35.8}{\pi }$$

Divide 35.8 by \pi .

$$R^{2}=\frac{179}{5\pi }$$

Take the square root of both sides of the equation.

$$R=\frac{179}{\sqrt{895\pi }} R=-\frac{179}{\sqrt{895\pi }}$$

Steps Using the Quadratic Formula

Subtract 35.8 from both sides.

$$\pi R^{2}-35.8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -35.8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R=\frac{0±\sqrt{0^{2}-4\pi \left(-35.8\right)}}{2\pi }$$

Square 0.

$$R=\frac{0±\sqrt{-4\pi \left(-35.8\right)}}{2\pi }$$

Multiply -4 times \pi .

$$R=\frac{0±\sqrt{\left(-4\pi \right)\left(-35.8\right)}}{2\pi }$$

Multiply -4\pi times -35.8.

$$R=\frac{0±\sqrt{\frac{716\pi }{5}}}{2\pi }$$

Take the square root of \frac{716\pi }{5}.

$$R=\frac{0±\frac{2\sqrt{895\pi }}{5}}{2\pi }$$

Now solve the equation R=\frac{0±\frac{2\sqrt{895\pi }}{5}}{2\pi } when ± is plus.

$$R=\frac{179}{\sqrt{895\pi }}$$

Now solve the equation R=\frac{0±\frac{2\sqrt{895\pi }}{5}}{2\pi } when ± is minus.

$$R=-\frac{179}{\sqrt{895\pi }}$$

The equation is now solved.

$$R=\frac{179}{\sqrt{895\pi }} R=-\frac{179}{\sqrt{895\pi }}$$