Question

arc length using radians
in circle o, angle aob measures $\frac{pi}{4}$ radians.
what is the length of arc ab?
$squarepi$ in.

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle with radius $r$ and central - angle $\theta$ (in radians) is $s = r\theta$.

Step2: Identify values of $r$ and $\theta$

From the problem, the radius of the circle $r = 16$ inches and the central - angle $\theta=\frac{\pi}{4}$ radians.

Step3: Calculate the arc length

Substitute $r = 16$ and $\theta=\frac{\pi}{4}$ into the formula $s = r\theta$. We get $s=16\times\frac{\pi}{4}$.
$s = 4\pi$ inches.

Answer:

$4\pi$