P6 / Random #2

Question:

Two wheels with centres A and B are touching each other as shown in Figure 1. Each wheel is of radius 7 cm.
(a) Find the area of the shaded part.
(b) The wheels turn along the straight line XY in opposite directions as shown in Figure 1. Find the distance between A and B when each wheel has made 5 complete turns. (The new position, not drawn to scale, is shown in Figure 2.)
(Take π = 22/7)

Solution: