Question

find the length of the arc. use 3.14 for the value of π. round your answer to the nearest tenth.
6 in
210°
a. 22.0 in
b. 110.9 in
c. 113.1 in
d. 120.4 in

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc 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. The conversion formula is $\theta_{rad}=\frac{\pi}{180}\times\theta_{deg}$. Given $\theta_{deg}=210^{\circ}$ and $r = 6$ inches.
$\theta=\frac{210\times\pi}{180}=\frac{7\pi}{6}$ radians.

Step2: Calculate the arc - length

Substitute $r = 6$ and $\theta=\frac{7\pi}{6}$ into the arc - length formula $s=r\theta$.
$s=6\times\frac{7\pi}{6}=7\pi$.

Step3: Substitute the value of $\pi$

Given $\pi = 3.14$, then $s=7\times3.14 = 21.98\approx22.0$ inches.

Answer:

A. 22.0 in