Question

The area of a circle is 81pie square feet. What is the length of the radius? What is the length of the diameter? Please show steps!

Answer 1

$A=81\pi \\A=\pi r^2 \\81\pi=\pi r^2\Longrightarrow r^2=81radius=\sqrt{81}=\boxed{9} \\diameter=2radius = 2\cdot9=\boxed{18}$

Answer 2

$\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=81\pi \end{cases}\implies 81\pi =\pi r^2\implies \cfrac{81\pi }{\pi }=r^2\implies 81=r^2 \\\\\\ \sqrt{81}=r\implies \boxed{9=r}~\hspace{10em}\stackrel{\textit{diameter = twice the radius}}{18}$