First of all, let's recall that the full circumference is
[tex] C = 2\pi r [/tex]
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
[tex] A = \cfrac{C}{12} = \cfrac{2 \pi r}{12} = \cfrac{\pi r}{6} [/tex]
Since we know the arc length, we can build and solve the following equation:
[tex] \cfrac{\pi r}{6} = 2\pi \iff \cfrac{r}{6} = 2 \iff r = 12[/tex]
