Question

the diameter of a circle is 2 meters. what is the area of a sector bounded by a 45° arc?
d=2 m
45°
give the exact answer in simplest form.
square meters

Explanation:

Step1: Find the radius of the circle

The formula for the radius \(r\) of a circle given the diameter \(d\) is \(r=\frac{d}{2}\). Given \(d = 2\) meters, then \(r=\frac{2}{2}=1\) meter.

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 \(\theta = 45^{\circ}\) and \(r = 1\) meter. Substitute these values into the formula:

$$
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Answer:

\(\frac{1}{8}\pi\)