Question

the radius of a circle is 1 meter. what is the area of a sector bounded by a 180° arc?
r=1 m
180°
give the exact answer in simplest form.
square meters

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector 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.

Step2: Substitute the given values into the formula

Given \(\theta = 180^{\circ}\) and \(r = 1\)m. Substitute these into the formula: \(A=\frac{180}{360}\times\pi\times(1)^{2}\).

Step3: Simplify the expression

\(\frac{180}{360}=\frac{1}{2}\), and \((1)^{2}=1\). So \(A=\frac{1}{2}\times\pi\times1=\frac{\pi}{2}\) square meters.

Answer:

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