MATH SOLVE

3 months ago

Q:
# In a circle, a 90 degree sector has area of 36pi ftsqd. what is the radius of the circle?

Accepted Solution

A:

[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]