Question

In a circle, a 90° sector has area 36π ft2. What is the radius of the circle?

Answer 1

Answer: The radius is 12 feet

Explanation:

You know that the formula used to calculate the area the a sector of a circle is:

`A=(C\pi )/(360)*r^2`

Where C is the central angle in degrees and r is the radius of the circle

Solve for "r" from this formula:

`360*A=C\pi*r^2\\\\(360*A)/(C\pi)=r^2\\\\r=\sqrt{(360*A)/(C\pi)}`

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:

`r=\sqrt{(360(36\pi ft^2))/(90\°\pi)}=12ft`