Solve 4pir^2=3pi

$$4 \pi r ^ { 2 } = 3 \pi$$

Solve for r

$$r=\frac{\sqrt{3}}{2}\approx 0.866025404$$

$$r=-\frac{\sqrt{3}}{2}\approx -0.866025404$$

Steps by Finding Square Root

Cancel out \pi on both sides.

$$4r^{2}=3$$

Divide both sides by 4.

$$r^{2}=\frac{3}{4}$$

Take the square root of both sides of the equation.

$$r=\frac{\sqrt{3}}{2} r=-\frac{\sqrt{3}}{2}$$

Steps Using the Quadratic Formula

Cancel out \pi on both sides.

$$4r^{2}=3$$

Divide both sides by 4.

$$r^{2}=\frac{3}{4}$$

Subtract \frac{3}{4} from both sides.

$$r^{2}-\frac{3}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{3}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-\frac{3}{4}\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-\frac{3}{4}\right)}}{2}$$

Multiply -4 times -\frac{3}{4}.

$$r=\frac{0±\sqrt{3}}{2}$$

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

$$r=\frac{\sqrt{3}}{2}$$

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

$$r=-\frac{\sqrt{3}}{2}$$

The equation is now solved.

$$r=\frac{\sqrt{3}}{2} r=-\frac{\sqrt{3}}{2}$$