Question

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

Answer 1

Answer: 300
`\pi`

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 ((x)/(360))`

`50\pi =2\pi r((60)/(360))`

Cancel the
`\pi` and simplify the fraction.

`50 = 2r((1)/(6))`

Simplify further.

`50 = r((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`