Central angles, their arcs and the areas of the sectors formed are all proportional:
central angle arc length area of sector
------------------ = ------------- = ------------------
2pi or 360 degrees Circumference area of the circle
For your problem, which references central angles and arc length we will use the first two fractions:
central angle arc length
------------------ = -------------
2pi or 360 degrees Circumference
Since your central angle is expressed in degrees we will use 360 in the denominator of the first fraction:
which simplifies to:
Cross multiplying we get:
Dividing by 12 we get:
All that's left is to replace with a decimal (3.14158....) and simplify the fraction. I'll leave that up to you.