Question

find the length s of the circular arc shown in the following figure. resources read it watch it

Explanation:

Step1: Convert angle to radians

We know that to convert degrees to radians, we use the formula $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta_{deg} = 110^{\circ}$, then $\theta_{rad}=110\times\frac{\pi}{180}=\frac{11\pi}{18}$.

Step2: Use arc - length formula

The formula for the length of a circular arc is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians. Here, $r = 6$ and $\theta=\frac{11\pi}{18}$. So, $s=6\times\frac{11\pi}{18}$.

Step3: Simplify the expression

$6\times\frac{11\pi}{18}=\frac{66\pi}{18}=\frac{11\pi}{3}$.

Answer:

$\frac{11\pi}{3}$