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

Step-by-step explanation:

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

$A=\frac{C\pi }{360}*r^2$

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

Solve for "r" from this formula:

$360*A=C\pi*r^2\\\\\frac{360*A}{C\pi}=r^2\\\\r=\sqrt{\frac{360*A}{C\pi}}$

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:

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