Question

if a circle has a radius of 7 meters and a central angle of 60°, what is the length of the arc? a. \\( \frac{\pi}{3} \\) meters b. 14\\( \pi \\) meters c. 7 meters d. \\( \frac{7\pi}{3} \\) meters

Explanation:

Step1: Convert degree to radian

The formula to convert degrees to radians is $\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}$. Given $\theta = 60^{\circ}$, then $\theta_{rad}=\frac{\pi}{180}\times60=\frac{\pi}{3}$ radians.

Step2: Use the arc - length formula

The arc - length formula is $s = r\theta$ (where $s$ is the arc length, $r$ is the radius, and $\theta$ is the central angle in radians). Given $r = 7$ meters and $\theta=\frac{\pi}{3}$ radians. Substitute the values into the formula: $s=7\times\frac{\pi}{3}=\frac{7\pi}{3}$ meters.

Answer:

d. $\frac{7\pi}{3}$ meters