Question

the measure of central xyz angle is $\frac{3\pi}{4}$ radians. what is the area of the shaded sector? $85\pi$ units² $256\pi$ units² $32\pi$ units² $96\pi$ units²

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{1}{2}r^{2}\theta\), 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, \(r = 16\) and \(\theta=\frac{3\pi}{4}\).

Step3: Substitute the values into the formula

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Answer:

\(96\pi\) units\(^{2}\)