Question

A circle with circumference12 has an arc with a 330∘ degree central angle. What is the length of the arc?

Answer 1

The formula for arc length which is measured in units not degrees is $\frac{ \beta }{360} *2 \pi r$, where 2 pi r is the circumference.  We were given the circumference as 12 pi, so we can fill in the rest of the formula and the find the length of the arc that is intercepted by that 330° angle.  $\frac{330}{360} *12 \pi$ gives us, after multiplying in the pi, an arc length of 34.56 units.