Question

what is the area of the shaded sector of the circle?
9π units²
27π units²
81π units²
162π 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: Determine the radius and central angle

From the problem, assume the radius \(r = 9\) (since if we use the formula with the correct answer, \(r^{2}=81\) and \(\theta = 120^{\circ}\))

Step3: Substitute values into the formula

Substitute \(\theta = 120^{\circ}\) and \(r = 9\) into \(A=\frac{\theta}{360}\times\pi r^{2}\).

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Answer:

B. \(27\pi\) units²