Respuesta :
[tex]\bf \textit{area of a sector of a circle}\\\\
A=\cfrac{\theta \pi r^2}{360}\quad
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad degrees\\
------\\
\theta =90\\
A=36\pi
\end{cases}\implies 36\pi =\cfrac{90\pi r^2}{360}
\\\\\\
\cfrac{36\pi }{90\pi }=\cfrac{r^2}{360}\implies \cfrac{2}{5}=\cfrac{r^2}{360}\implies \cfrac{360\cdot 2}{5}=r^2\implies 144=r^2
\\\\\\
\sqrt{144}=r\implies 12=r[/tex]
The radius of the circle is 12 ft.
Quarter circle
Each quarter of a circle is formed when a circle is split into four equal sections. Each quarter of the circle is referred to as a quadrant. As a result, the area of a quarter circle equals four times the circle's area.
Area = π×r²/4
Where, r is the radius of the circle.
How to find the radius?
A 90° sector of a circle is called a quarter circle.
The area given in this sector is 36π ft².
then,
[tex]\frac{\pi r^{2}}{4} =36\pi[/tex]
[tex]r^{2}=144[/tex]
[tex]r= 12 \text{ ft}[/tex]
Hence the radius is 12 ft.
Learn more about the area of circle here- https://brainly.com/question/14068861
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