Question

the diameter of a circle is 2 miles. what is the area of a sector bounded by a 108° arc?
give the exact answer in simplest form.
square miles

Explanation:

Step1: Find the radius of the circle

The formula for radius \(r\) is \(r=\frac{d}{2}\). Given \(d = 2\) miles, so \(r=\frac{2}{2}=1\) mile.

Step2: Use the sector - area formula

The formula for the area of a sector is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta = 108^{\circ}\) and \(r = 1\) mile.
Substitute the values: \(A=\frac{108}{360}\times\pi\times(1)^{2}\).
Simplify \(\frac{108}{360}=\frac{3}{10}\).
So \(A=\frac{3}{10}\pi\) square miles.

Answer:

\(\frac{3}{10}\pi\)