Solve 10=pi*R^2

$$10 = \pi \times R ^ { 2 }$$

Solve for R

$$R=\sqrt{\frac{10}{\pi }}\approx 1.784124116$$

$$R=-\sqrt{\frac{10}{\pi }}\approx -1.784124116$$

Steps by Finding Square Root

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

$$\pi R^{2}=10$$

Divide both sides by \pi .

$$\frac{\pi R^{2}}{\pi }=\frac{10}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$R^{2}=\frac{10}{\pi }$$

Take the square root of both sides of the equation.

$$R=\frac{10}{\sqrt{10\pi }} R=-\frac{10}{\sqrt{10\pi }}$$

Steps Using the Quadratic Formula

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

$$\pi R^{2}=10$$

Subtract 10 from both sides.

$$\pi R^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R=\frac{0±\sqrt{0^{2}-4\pi \left(-10\right)}}{2\pi }$$

Square 0.

$$R=\frac{0±\sqrt{-4\pi \left(-10\right)}}{2\pi }$$

Multiply -4 times \pi .

$$R=\frac{0±\sqrt{\left(-4\pi \right)\left(-10\right)}}{2\pi }$$

Multiply -4\pi times -10.

$$R=\frac{0±\sqrt{40\pi }}{2\pi }$$

Take the square root of 40\pi .

$$R=\frac{0±2\sqrt{10\pi }}{2\pi }$$

Now solve the equation R=\frac{0±2\sqrt{10\pi }}{2\pi } when ± is plus.

$$R=\frac{10}{\sqrt{10\pi }}$$

Now solve the equation R=\frac{0±2\sqrt{10\pi }}{2\pi } when ± is minus.

$$R=-\frac{10}{\sqrt{10\pi }}$$

The equation is now solved.

$$R=\frac{10}{\sqrt{10\pi }} R=-\frac{10}{\sqrt{10\pi }}$$