Question

question 7 of 10 in the diagram below, what is the approximate length of the minor - arc de? 120° f 25 cm a. 52 cm b. 26 cm c. 79 cm d. 39 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 $\theta_{deg}=120^{\circ}$, then $\theta_{rad}=120\times\frac{\pi}{180}=\frac{2\pi}{3}$. The radius $r = 25$ cm.

Step2: Calculate the arc - length

Substitute $r = 25$ cm and $\theta=\frac{2\pi}{3}$ into the arc - length formula $s=r\theta$. So $s = 25\times\frac{2\pi}{3}=\frac{50\pi}{3}\approx\frac{50\times3.14}{3}=\frac{157}{3}\approx52.33$ cm.

Answer:

A. 52 cm