Question

the radius of the circle shown below is 8 centimeters. what is the approximate length of $overparen{xy}$? 115° a. 16.1 cm b. 50.3 cm c. 64.2 cm d. 8.0 cm

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central - angle in radians. First, convert the angle from degrees to radians. We know that to convert degrees to radians, we use the conversion factor $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg}=115^{\circ}$, then $\theta_{rad}=115\times\frac{\pi}{180}=\frac{115\pi}{180}=\frac{23\pi}{36}$ radians, and $r = 8$ cm.

Step2: Calculate the arc - length

Substitute $r = 8$ and $\theta=\frac{23\pi}{36}$ into the arc - length formula $s=r\theta$. So $s = 8\times\frac{23\pi}{36}=\frac{46\pi}{9}\approx\frac{46\times3.14}{9}=\frac{144.44}{9}\approx16.05\approx16.1$ cm.

Answer:

A. 16.1 cm