Question

in the diagram below, what is the approximate length of the minor arc xy? 27 cm 60° a. 28.3 cm b. 14.1 cm c. 25.7 cm d. 56.5 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.

Step2: Convert degrees to radians

Given $\theta=60^{\circ}$, we convert it to radians. Since $180^{\circ}=\pi$ radians, then $60^{\circ}=\frac{\pi}{3}$ radians. The radius $r = 27$ cm.

Step3: Calculate arc - length

Substitute $r = 27$ cm and $\theta=\frac{\pi}{3}$ into the arc - length formula $s=r\theta$. So $s = 27\times\frac{\pi}{3}=9\pi\approx9\times3.14 = 28.26\approx28.3$ cm.

Answer:

A. 28.3 cm