Question

in the diagram below, what is the approximate length of the minor arc $widehat{ab}$? a. 31 cm b. 63 cm c. 21 cm d. 42 cm

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc of a circle is $s = r\theta$, where $s$ is the arc - length, $r$ 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 $120^{\circ}=120\times\frac{\pi}{180}=\frac{2\pi}{3}$ radians, and $r = 20$ cm.

Step2: Substitute values into formula

Substitute $r = 20$ cm and $\theta=\frac{2\pi}{3}$ into the arc - length formula $s=r\theta$. So $s = 20\times\frac{2\pi}{3}=\frac{40\pi}{3}\approx\frac{40\times3.14}{3}\approx41.87\approx42$ cm.

Answer:

D. 42 cm