Question

the measure of central angle abc is \\(\frac{pi}{2}\\) radians. what is the area of the shaded sector? \\(\bigcirc\\) \\(6pi\\) units\\(^2\\) \\(\bigcirc\\) \\(9pi\\) units\\(^2\\) \\(\bigcirc\\) \\(18pi\\) units\\(^2\\) \\(\bigcirc\\) \\(36pi\\) units\\(^2\\)

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, \(r = 6\) and \(\theta=\frac{\pi}{2}\).

Step3: Substitute the values into the formula

Substitute \(r = 6\) and \(\theta=\frac{\pi}{2}\) into \(A=\frac{1}{2}r^{2}\theta\).

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Answer:

\(9\pi\) units\(^{2}\) (the second option)