Question

in circle o, angle aob measures $\frac{pi}{4}$ radians. what is the length of arc ab? $square pi$ in. (there is a circle with center o, points a and b on the circle, oa and ob are radii with length 16 in, angle aob is $\frac{pi}{4}$ radians)

Explanation:

Step1: Recall arc length formula

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

Step2: Identify radius and angle

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

Step3: Calculate arc length

Substitute \( r = 16 \) and \( \theta=\frac{\pi}{4} \) into the formula \( s = r\theta \). So \( s=16\times\frac{\pi}{4} \). Simplifying \( 16\times\frac{\pi}{4} \), we divide 16 by 4 to get 4, so \( s = 4\pi \).

Answer:

\( 4 \)