consider circle y with radius 3 m and central angle xyz measuring 70°. what is the approximate length of…

Answer:

B. 3.7 meters

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 $\theta_{deg} = 70^{\circ}$, then $\theta_{rad}=70\times\frac{\pi}{180}=\frac{7\pi}{18}$ radians, and $r = 3$ m.

Step2: Calculate arc - length

Substitute $r = 3$ and $\theta=\frac{7\pi}{18}$ into the arc - length formula $s=r\theta$. So $s=3\times\frac{7\pi}{18}=\frac{7\pi}{6}\approx\frac{7\times3.14}{6}=\frac{21.98}{6}\approx3.7$ m.