Question

If a circle has area $81\mathrm{\pi }$ square inches, what is the radius?

Answer 1

What is the radius of a circle:

The area of the circle is,

$A={\mathrm{\pi r}}^2$

Substitute the values in the formula.

$\begin{array}{rcl}81\mathrm{\pi }& =& {\mathrm{\pi r}}^2\\ & \Rightarrow & {\mathrm{\pi r}}^2=81\mathrm{\pi }\\ & \Rightarrow & {\mathrm{r}}^2=81\\ \therefore \mathrm{r}& =& \pm 9\end{array}$

The radius cannot be negative. Therefore, the only solution is $9$ inches.

Hence, the radius of the circle is $\mathbf{9}$ inches.