Question

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

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{1}{2}r^{2}\theta\), 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 \(r = 6\) and the central angle \(\theta=\frac{\pi}{2}\) radians.

Step3: Substitute the values into the formula

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

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Answer:

\(9\pi\) units\(^{2}\)