Given:
a.) A circle has a radius of 20 cm.
b.) It has a central angle that measures 216 degrees.
Let's draw the figure to better understand the scenario:
For us to be able to determine the arc length, we will be using the following formula:
[tex]\text{ Arc Length = }\frac{\Theta}{360\degree}2\pi r[/tex]Where,
r = radius of the circle
Θ = central angle
We get,
[tex]\text{ Arc Length = }\frac{216\degree}{360\degree}2\pi(20)[/tex][tex]\text{ = }\frac{3}{5}\text{ \lparen40}\pi)[/tex][tex]\text{ = }\frac{120}{5}\pi[/tex][tex]\text{ Arc Length = 24}\pi\text{ cm or 24\lparen3.14\rparen = 75.36 cm}[/tex]Therefore, the length of the arc is 24π cm or 75.36 cm
