Question

the radius of a circle is 4 miles. what is the length of a 135° arc?
r=4 mi
135°
give the exact answer in simplest form.
miles

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is $L = \frac{\theta}{360^\circ} \times 2\pi r$, where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.

Step2: Substitute given values

Here, $\theta = 135^\circ$ and $r = 4$ miles. Substitute these into the formula:
$L = \frac{135^\circ}{360^\circ} \times 2\pi \times 4$

Step3: Simplify the expression

First, simplify $\frac{135}{360} = \frac{3}{8}$. Then, $2\times4 = 8$. So the expression becomes $\frac{3}{8} \times 8\pi$. The 8 in the numerator and denominator cancels out, leaving $3\pi$.

Answer:

$3\pi$