Doug C. answered • 09/20/22
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The circumference of a circle with radius 11km is 2πr (or 22π km in this case).
A central angle of 12 degrees subtends an arc that is 12/360 or 1/30 of the entire circumference.
1/30 of 22π is 22π/30 or 11π/15 km.
You might have seen the formula as s = (θ/360) (2πr) = (θ/180) (πr). Probably better to just logically think through it as opposed to trying to memorize that formula, i.e. the central angle gives a fraction of the circumference.
Similar logic leads to finding the area of a sector--central angle used to give fraction of the area of the entire circle.
