Question

finding arc length using radians
in circle o, angle aob measures $\frac{pi}{4}$ radians.
what is the length of arc ab?
$square pi$ in.
(note: the circle has center o, radius ob is 16 in, and central angle aob is $\frac{pi}{4}$ radians)

Explanation:

Step1: Recall arc length formula

The formula for arc length \(s\) when the central angle \(\theta\) is in radians is \(s = r\theta\), where \(r\) is the radius of the circle.

Step2: Identify given values

The radius \(r = 16\) in, and the central angle \(\theta = \frac{\pi}{4}\) radians.

Step3: Substitute values into formula

\[
s = 16 \times \frac{\pi}{4}
\]

Step4: Calculate the numerical coefficient

\[
16 \times \frac{1}{4} = 4
\]
So \(s = 4\pi\) in.

Answer:

\(4\pi\) in. (the blank should be filled with 4)