Question

a runner completes a 300° arc on a circular track of radius 50 meters. how long is the arc? a. 75π meters b. 250π/3 meters c. 300π/3 meters d. 150π/3 meters

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc \(s\) 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 \(\theta\) (in radians) \(=\frac{\pi}{180}\times\theta\) (in degrees). Given \(\theta = 300^{\circ}\), then \(\theta=\frac{300\pi}{180}=\frac{5\pi}{3}\) radians, and \(r = 50\) meters.

Step2: Substitute values into the arc - length formula

Substitute \(r = 50\) and \(\theta=\frac{5\pi}{3}\) into \(s=r\theta\). So \(s = 50\times\frac{5\pi}{3}=\frac{250\pi}{3}\) meters.

Answer:

B. \(\frac{250\pi}{3}\) meters