Question

find the length of arc abc. use 3.14 for the value of π. 6.1 cm 240° round to the nearest hundredth of a 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 to convert degrees to radians, we use the conversion factor $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg}=240^{\circ}$, then $\theta_{rad}=240\times\frac{\pi}{180}=\frac{4\pi}{3}$.

Step2: Identify the radius

The radius of the circle $r = 6.1$ cm.

Step3: Calculate the arc - length

Substitute $r = 6.1$ cm and $\theta=\frac{4\pi}{3}$ into the arc - length formula $s = r\theta$. So $s=6.1\times\frac{4\pi}{3}$. Since $\pi = 3.14$, we have $s = 6.1\times\frac{4\times3.14}{3}=6.1\times\frac{12.56}{3}=\frac{76.616}{3}\approx25.54$ cm.

Answer:

$25.54$ cm