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$^2$

Question

Accepted Answer

# 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 $A=\frac{1}{2}r^{2}\theta$.
$$
\begin{align*}
A&=\frac{1}{2}\times6^{2}\times\frac{\pi}{2}\
&=\frac{1}{2}\times36\times\frac{\pi}{2}\
&= 9\pi
\end{align*}
$$

# Answer:
$9\pi$ units$^{2}$ (the second option)

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the area of a sector

Step2: Identify the values of \(r\) and \(\theta\)

Step3: Substitute the values into the formula

Answer: