Question

In a circle, a 90° sector has an area of 36π in2. What is the radius of this circle?

Answer 1

Answer:

r = 12 in

Step-by-step explanation:

$A = \frac{1}{4} r^{2} \pi \\\\r = \sqrt{\frac{4A}{\pi } } = \sqrt{\frac{4 * 36\pi }{\pi } } = 2 * 6 = 12\ in$

Answer 2

Answer:

r = 12 in

Step-by-step explanation:

recall that a full circle is represented by a sector that is 360°

in our case, the given sector is 90°

Hence our sector is 90° / 360° = 1/4 of a circle

It is also given that our 90° sector (which we now know is 1/4 of a circle) has an area of 36π in² and recall that the area of a full circle is πr²   (where r is the radius).

Hence,

πr² = 4 x area of 90° sector

πr² = 4 x 36π

πr² = 144π  (divide both sides by π)

r² = 144

r = √144

r = 12 in