Question

What is the radius of a circle in which a 30° arc is 2π inches long?

Answer 1

First of all, let's recall that the full circumference is

$C = 2\pi r$

Now, since 30 is one twelfth of 360, a 30° arc will be one twelfth of the whole circumference. So, if you call the arc length A, you have

$A = \cfrac{C}{12} = \cfrac{2 \pi r}{12} = \cfrac{\pi r}{6}$

Since we know the arc length, we can build and solve the following equation:

$\cfrac{\pi r}{6} = 2\pi \iff \cfrac{r}{6} = 2 \iff r = 12$