Answer: The radius is 12 feet
Step-by-step explanation:
You know that the formula used to calculate the area the a sector of a circle is:
[tex]A=\frac{C\pi }{360}*r^2[/tex]
Where C is the central angle in degrees and r is the radius of the circle
Solve for "r" from this formula:
[tex]360*A=C\pi*r^2\\\\\frac{360*A}{C\pi}=r^2\\\\r=\sqrt{\frac{360*A}{C\pi}}[/tex]
You know the that the angle is 90 degrees and you know that the area of the sector is 36π ft², then substituting values you get that the radius of this circle is:
[tex]r=\sqrt{\frac{360(36\pi ft^2)}{90\°\pi}}=12ft[/tex]
