Question

what is the area of the shaded sector of the circle? 20π units² 40π units² 180π units² 400π units²

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle of the sector and \(r\) is the radius of the circle.

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

From the problem, \(\theta = 162^{\circ}\) and \(r = 20\).

Step3: Substitute the values into the formula

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Answer:

\(180\pi\) units\(^{2}\) (the third option)