Question

the radius of a circle is 2 inches. what is the area of a sector bounded by a 180° arc?
r=2 in
180°
give the exact answer in simplest form.
square inches

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{\theta}{360^{\circ}}\times\pi r^{2}\), 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 that \(\theta = 180^{\circ}\) and \(r = 2\) inches.
Substitute these values into the formula: \(A=\frac{180^{\circ}}{360^{\circ}}\times\pi\times(2)^{2}\).
Simplify \(\frac{180^{\circ}}{360^{\circ}}=\frac{1}{2}\), and \((2)^{2}=4\).
So \(A=\frac{1}{2}\times\pi\times4\).

Step3: Calculate the value of the area

\(\frac{1}{2}\times4 = 2\), so \(A = 2\pi\).

Answer:

\(2\pi\)