in circle j with ( mangle hjk = 66^{circ} ) and ( hj = 11 ), find the area of sector hjk. round to the nearest hundredth.

Question

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 $A=\frac{\theta}{360}\times\pi r^{2}$, where $\theta$ is the central - angle in degrees and $r$ is the radius of the circle.
## Step2: Identify the values of $\theta$ and $r$
Given that $\theta = m\angle HJK=66^{\circ}$ and $r = HJ = 11$.
## Step3: Substitute the values into the formula
Substitute $\theta = 66$ and $r = 11$ into the formula $A=\frac{\theta}{360}\times\pi r^{2}$.
$$
\begin{align*}
A&=\frac{66}{360}\times\pi\times(11)^{2}\
&=\frac{66}{360}\times\pi\times121\
&=\frac{66\times121\pi}{360}\
&=\frac{7986\pi}{360}\
&=\frac{1331\pi}{60}
\end{align*}
$$
## Step4: Calculate the numerical value
Using $\pi\approx3.14159$, we have $A=\frac{1331\times3.14159}{60}$.
$$
\begin{align*}
A&=\frac{4181.45629}{60}\
&\approx69.69
\end{align*}
$$

# Answer:
$69.69$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the area of a sector

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

Step3: Substitute the values into the formula

Step4: Calculate the numerical value

Answer: