a wiper moves 135* (*= degrees) top end 23 in. from pivot point, bottom end 9 in. from pivot point. how much greater is the length of arc traced by top than of bottom?

Question

a wiper moves 135* (*= degrees) top end 23 in. from pivot point, bottom end 9 in. from pivot point. how much greater is the length of arc traced by top than of bottom?

Answer 1

When we are looking at arc length we are talking about circumference which is 2 pi r and what portion of the circumference our angle sub tends. In this case it is 135/360=3/8

The arc of the larger circle would be (2pi)(23)(3/8)=54.2

The arc of the smaller circle would be (2pi)(9)(3/8) 21.2

The difference is 54.2 - 21.2 = 30cm