Question

the diameter of a circle is 12 miles. what is the area of a sector bounded by a 135° arc?
give the exact answer in simplest form.
square miles

Explanation:

Step1: Find the radius of the circle

The formula for the radius \(r\) of a circle given the diameter \(d\) is \(r=\frac{d}{2}\).
Since \(d = 12\) miles, then \(r=\frac{12}{2}=6\) miles.

Step2: Use the sector - area formula

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.
We know that \(\theta = 135^{\circ}\) and \(r = 6\) miles.
Substitute these values into the formula:

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Answer:

\(\frac{27\pi}{2}\)