Question

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

Explanation:

Step1: Recall sector - area formula

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 values into the formula

$A=\frac{1}{2}(16)^{2}\times\frac{3\pi}{4}$.
First, calculate $(16)^{2}=256$. Then, $\frac{1}{2}\times256 = 128$.
Next, $128\times\frac{3\pi}{4}=\frac{128\times3\pi}{4}=96\pi$.

Answer:

$96\pi$ units$^{2}$