Question

If an arc of 60 degrees has an arc length of 50pi what is the circumference

Answer 1

Answer: 300$\pi$

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$\pi$ and the arc is 60°

Arc-length = $2\pi r (\frac{x}{360})$

$50\pi =2\pi r(\frac{60}{360})$

Cancel the $\pi$ and simplify the fraction.

$50 = 2r(\frac{1}{6})$

Simplify further.

$50 = r(\frac{1}{3} )$

Pass the 3 to the other side.

$150=r$

So our radius is 150.

To find the circumference, we use the formula $2\pi r$

Plug in r.

$2\pi (150) = 300\pi$