the radius of a circle is 2 miles. what is the area of a sector bounded by a 90° arc?
r=2 mi
90°
give the exact answer in simplest form.
square miles

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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 of the sector and $r$ is the radius of the circle.
## Step2: Substitute the given values into the formula
Given that $\theta = 90^{\circ}$ and $r = 2$ miles.
$$
\begin{align*}
A&=\frac{90^{\circ}}{360^{\circ}}\times\pi\times(2)^{2}\
&=\frac{1}{4}\times\pi\times4\
&=\pi
\end{align*}
$$

# Answer:
$\pi$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the area of a sector

Step2: Substitute the given values into the formula

Answer: