if an arc of 60 degrees has an arc length of 50pi what is the circumference Question if an arc of 60 degrees has an arc length of 50pi what is the circumference in progress 0 Math Samantha 3 months 2022-02-15T07:04:33+00:00 2022-02-15T07:04:33+00:00 1 Answer 0 views 0

## Answers ( )

Answer:300[tex]\pi[/tex]Step-by-step explanation:Let’s use the arc-length formula to solve this problem, and plug in the values that we have. Arc length is 50[tex]\pi[/tex] and the arc is 60°

Arc-length = [tex]2\pi r (\frac{x}{360})[/tex]

[tex]50\pi =2\pi r(\frac{60}{360})[/tex]

Cancel the [tex]\pi[/tex] and simplify the fraction.

[tex]50 = 2r(\frac{1}{6})[/tex]

Simplify further.

[tex]50 = r(\frac{1}{3} )[/tex]

Pass the 3 to the other side.

[tex]150=r[/tex]

So our radius is 150.

To find the circumference, we use the formula [tex]2\pi r[/tex]

Plug in r.

[tex]2\pi (150) = 300\pi[/tex]