We can use the formula s = rθ, where s is the arc length, r is the radius, and θ is the RADIAN measure of the central angle.
In this problem, r = 11 and θ = π/6.
So, s = 11(π/6) = 11π/6
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In case you forget the formula under pressure (like during an exam!), here is another approach:
There are 360° in a circle.
360°/30° = 12 The number of degrees in an arc of a circle is the same as the number of degrees in the central angle determined by the arc. So, the length of the arc cut off by the central angle is 1/12 of the length of the entire circle. The length of the circle is the circumference, 2πr.
Therefore, s = (1/12)(circumference)
= (1/12)(2π)(11) = 11π/6
