Solve pir^2=78.54

$$\pi r ^ { 2 } = 78.54$$

Solve for r

$$r = \frac{\sqrt{\frac{7854}{\pi}}}{10} \approx 5.000005846$$

$$r = -\frac{\sqrt{\frac{7854}{\pi}}}{10} \approx -5.000005846$$

Steps by Finding Square Root

Divide both sides by \pi .

$$\frac{\pi r^{2}}{\pi }=\frac{78.54}{\pi }$$

Dividing by \pi undoes the multiplication by \pi .

$$r^{2}=\frac{78.54}{\pi }$$

Divide 78.54 by \pi .

$$r^{2}=\frac{3927}{50\pi }$$

Take the square root of both sides of the equation.

$$r=\frac{3927}{5\sqrt{7854\pi }} r=-\frac{3927}{5\sqrt{7854\pi }}$$

Steps Using the Quadratic Formula

Subtract 78.54 from both sides.

$$\pi r^{2}-78.54=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \pi for a, 0 for b, and -78.54 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\pi \left(-78.54\right)}}{2\pi }$$

Square 0.

$$r=\frac{0±\sqrt{-4\pi \left(-78.54\right)}}{2\pi }$$

Multiply -4 times \pi .

$$r=\frac{0±\sqrt{\left(-4\pi \right)\left(-78.54\right)}}{2\pi }$$

Multiply -4\pi times -78.54.

$$r=\frac{0±\sqrt{\frac{7854\pi }{25}}}{2\pi }$$

Take the square root of \frac{7854\pi }{25}.

$$r=\frac{0±\frac{\sqrt{7854\pi }}{5}}{2\pi }$$

Now solve the equation r=\frac{0±\frac{\sqrt{7854\pi }}{5}}{2\pi } when ± is plus.

$$r=\frac{3927}{5\sqrt{7854\pi }}$$

Now solve the equation r=\frac{0±\frac{\sqrt{7854\pi }}{5}}{2\pi } when ± is minus.

$$r=-\frac{3927}{5\sqrt{7854\pi }}$$

The equation is now solved.

$$r=\frac{3927}{5\sqrt{7854\pi }} r=-\frac{3927}{5\sqrt{7854\pi }}$$