Find the length l of one "arch" of this cycloid, that is, find the distance traveled by a small stone stuck in the tread of a tire of radius r during one revolution of the rolling tire.

If there is no slipping or skidding going on, then for each revolution, the tire rolls along the ground a distance equal to the tire's circumference.

Circumference of the tire = 2 · π · Radius.

During the same revolution, the small stone stuck in the tread travels in a big semicircular arc that's (2 · π · r) long. (roughly 6.28r)