Question

1. in a circle, a 90° sector has area 36π ft². what is the radius of the circle?

12 ft
18 ft
6 ft
16 ft

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle of the sector and \(r\) is the radius of the circle. Given \(\theta = 90^{\circ}\) and \(A = 36\pi\) \(ft^{2}\).
Substitute \(\theta = 90^{\circ}\) into the formula: \(A=\frac{90}{360}\times\pi r^{2}=\frac{1}{4}\pi r^{2}\).

Step2: Solve for \(r\)

Since \(A = 36\pi\), we have the equation \(\frac{1}{4}\pi r^{2}=36\pi\).
First, divide both sides of the equation by \(\pi\): \(\frac{1}{4}r^{2}=36\).
Then multiply both sides by \(4\) to get \(r^{2}=144\).
Take the square root of both sides: \(r=\sqrt{144}\).

Answer:

\(12\) \(ft\)