geometry math problem

Question

the radius of a circle is 10 miles. What is the length of a 135° arc?

Answer 1

The full circumference - all 360° around - is equal to 2πr, where r is the radius. A 135° arc would have a length equal to 135/360 of the full circumference: 2πr·(135/360). Plug in the values for r (10 miles) and π (use the π button on your calculator) to get the answer.

Answer 2

length of arc = circumference * degree measure of arc/degrees in a circle

length of arc = circumference * 135/360

length of arc = 2 * PI * 20 * 135/360 = 70.65 miles