in circle b with m∠abc = 68° and ab = 16, find the area of sector abc. 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 of the sector and $r$ is the radius of the circle.

## Step2: Identify the values of $\theta$ and $r$
Given that $\theta = 68^{\circ}$ and $r = AB=16$

## Step3: Substitute the values into the formula
$$
\begin{align*}
A&=\frac{68}{360}\times\pi\times(16)^{2}\
&=\frac{68}{360}\times\pi\times256\
&=\frac{68\times256\pi}{360}\
&=\frac{17408\pi}{360}\
\end{align*}
$$

## Step4: Calculate the numerical value
$$
\begin{align*}
A&=\frac{17408\times3.14}{360}\
&=\frac{54661.12}{360}\
&\approx151.84
\end{align*}
$$

# Answer:
$151.84$

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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: