Question

the radius of a circle is 8 feet. what is the length of a 135° arc?
135°
r=8 ft
give the exact answer in simplest form.
feet
π
□/□
submit

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc is $L=\frac{\theta}{360^\circ}\times2\pi r$, where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.

Step2: Substitute values

Given $\theta = 135^\circ$ and $r = 8$ feet. Substitute these into the formula:
$L=\frac{135^\circ}{360^\circ}\times2\pi\times8$

Step3: Simplify the expression

First, simplify $\frac{135}{360}=\frac{3}{8}$. Then:
$L=\frac{3}{8}\times16\pi$ (since $2\times8 = 16$)
$\frac{3}{8}\times16\pi=6\pi$

Answer:

$6\pi$