If the arean of circle is 56 what is radius??

Jun 4, 2018

The radius of the circle is $\sqrt{\frac{A}{\pi}} \approx 4.2$.

Explanation:

The area of a circle is given by $\pi {r}^{2}$, where $r$ is the radius of the circle. We know what the area is, and $\pi$ is a constant, so we can solve for the radius:

$A = \pi {r}^{2} \rightarrow 56 = \pi {r}^{2} \rightarrow {r}^{2} = \frac{56}{\pi} \rightarrow r = \pm \sqrt{\frac{56}{\pi}} \approx 4.2$.

(We know we have to use the positive square root because a negative radius wouldn't make sense!)

Jun 4, 2018

$r = 2 \frac{\sqrt{14 \pi}}{\pi} \approx 4.22$

Explanation:

${A}_{\text{circle}} = \pi {r}^{2}$

$56 = \pi {r}^{2}$

$\frac{56}{\pi} = {r}^{2}$

$\pm \sqrt{\frac{56}{\pi}} = \sqrt{{r}^{2}}$

We can ignore the negative solution because a radius cannot be negative.

$r = 2 \frac{\sqrt{14 \pi}}{\pi}$

$r = 2 \frac{\sqrt{14 \pi}}{\pi} \approx 4.22$