Question

the measure of central angle rst is π radians. what is the area of the shaded sector? 4π units² 8π units² 16π units² 20π units²

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector is \(A=\frac{1}{2}r^{2}\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians.

Step2: Identify the values of \(r\) and \(\theta\)

From the problem, the radius \(r = 4\) and the central angle \(\theta=\pi\) radians.

Step3: Substitute the values into the formula

Substitute \(r = 4\) and \(\theta=\pi\) into the formula \(A=\frac{1}{2}r^{2}\theta\).
We get \(A=\frac{1}{2}\times4^{2}\times\pi\).
First, calculate \(4^{2}=16\). Then \(\frac{1}{2}\times16 = 8\). So \(A = 8\pi\) units\(^{2}\).

Answer:

B. \(8\pi\) units\(^{2}\)