Find the length s of the circular arc.

Question

Find the length s of the circular arc. (Assume r = 6 and θ = 110°.)

s = 

 

Answer 1

s = 6(360° - 110°)·π/180° ≈ 26.18

Answer 2

We should approach this problem by regarding the length of the arc, s, as a fraction of the circumference of the circle. Specifically, any arc represents x degrees out of the total 360° that comprise a circle. Thus, for any circle, the length of an arc can be represented as:

Arc Length = (x/360) * C

where C is the circumference of the circle and x is the angle of the arc.

Thus, we have:

s = ( (360 - θ) / 360 ) * (2 π r)

s = ( (360 - 110) / 360 ) * (2*6*π)

s = 26.18

I hope this helps!