Answer: 12 inches
Step-by-step explanation:
Given: In a circle , the area of a sector = [tex]36 \pi\text{ inches}[/tex]
Measure of Arc [tex]\theta=90^{\circ}[/tex]
The formula to calculate the area of the sector is given by:-
[tex]\text{ Area of sector}=\frac{\theta}{360^{\circ}}\times\pi r^2[/tex]
Substitute area and angle in the formula, we get
[tex]36\pi=\frac{90^{\circ}}{360^{\circ}}\times\pi r^2\\\\\Rightarrow36\pi=\frac{1}{4}\times\pi r^2\\\\\Rightarrow\ r^2=36\times4\\\\\Rightarrow r^2=144\\\\\Rightarrow\ r=12\ \text{ inches}[/tex]
Hence, the radius of the circle = 12 inches.
