Solve pir^2=48

$$\pi r ^ { 2 } = 48$$

Solve for r

$$r=4\sqrt{\frac{3}{\pi }}\approx 3.908820095$$

$$r=-4\sqrt{\frac{3}{\pi }}\approx -3.908820095$$

Steps by Finding Square Root

Divide both sides by \pi .

$$\frac{\pi r^{2}}{\pi }=\frac{48}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$r^{2}=\frac{48}{\pi }$$

Take the square root of both sides of the equation.

$$r=\frac{12}{\sqrt{3\pi }} r=-\frac{12}{\sqrt{3\pi }}$$

Steps Using the Quadratic Formula

Subtract 48 from both sides.

$$\pi r^{2}-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\pi \left(-48\right)}}{2\pi }$$

Square 0.

$$r=\frac{0±\sqrt{-4\pi \left(-48\right)}}{2\pi }$$

Multiply -4 times \pi .

$$r=\frac{0±\sqrt{\left(-4\pi \right)\left(-48\right)}}{2\pi }$$

Multiply -4\pi times -48.

$$r=\frac{0±\sqrt{192\pi }}{2\pi }$$

Take the square root of 192\pi .

$$r=\frac{0±8\sqrt{3\pi }}{2\pi }$$

Now solve the equation r=\frac{0±8\sqrt{3\pi }}{2\pi } when ± is plus.

$$r=\frac{12}{\sqrt{3\pi }}$$

Now solve the equation r=\frac{0±8\sqrt{3\pi }}{2\pi } when ± is minus.

$$r=-\frac{12}{\sqrt{3\pi }}$$

The equation is now solved.

$$r=\frac{12}{\sqrt{3\pi }} r=-\frac{12}{\sqrt{3\pi }}$$