Problem 25 (2013 AMC 8)

A ball with diameter $4$ inches starts at point $A$ to roll along the track shown. The track is comprised of $3$ semicircular arcs whose radii are $R_1 = 100$ inches, $R_2 = 60$ inches, and $R_3 = 80$ inches, respectively. The ball always remains in contact with the track and does not slip. What is the distance the center of the ball travels over the course from $A$ to $B$? [See figure in original PDF]