find the area of a sector of a circle with radius 12 inches subtended by a central angle of 240°. answer exactly in terms of pi. square inches question help: message instructor submit question

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Accepted Answer

# Explanation:
## Step1: Recall the formula for the area of a sector
The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central angle and $r$ is the radius.
## Step2: Substitute the given values into the formula
Given $r = 12$ inches and $\theta=240^{\circ}$.
$$
\begin{align*}
A&=\frac{240^{\circ}}{360^{\circ}}\times\pi\times(12)^{2}\
&=\frac{2}{3}\times\pi\times144
\end{align*}
$$
## Step3: Simplify the expression
$$
\begin{align*}
A&=\frac{2\times144}{3}\times\pi\
& = 96\pi
\end{align*}
$$

# Answer:
$96\pi$

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Question

Explanation:

Step1: Recall the formula for the area of a sector

Step2: Substitute the given values into the formula

Step3: Simplify the expression

Answer: