what is the area of a sector with a central angle of \frac{8\pi}{11} radians and a radius of 7.2 ft? use 3.14 for \pi and round your final answer to the nearest hundredth. enter your answer as a decimal in the box.

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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 is $A=\frac{1}{2}r^{2}\theta$, where $r$ is the radius and $\theta$ is the central angle in radians.
## Step2: Substitute the given values into the formula
Given $r = 7.2$ ft and $\theta=\frac{8\pi}{11}$. Substitute into $A=\frac{1}{2}r^{2}\theta$:
$$
\begin{align*}
A&=\frac{1}{2}\times(7.2)^{2}\times\frac{8\pi}{11}\
&=\frac{1}{2}\times51.84\times\frac{8\pi}{11}\
& = 25.92\times\frac{8\pi}{11}
\end{align*}
$$
## Step3: Substitute $\pi = 3.14$
$$
\begin{align*}
A&=25.92\times\frac{8\times3.14}{11}\
&=25.92\times\frac{25.12}{11}\
&=\frac{25.92\times25.12}{11}\
&=\frac{651.1264}{11}\
&\approx59.19
\end{align*}
$$

# Answer:
$59.19$

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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: Substitute \(\pi = 3.14\)

Answer: