AMC 8 2013 Problem 25

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?

$\textbf{(A)}\ 238\pi \textbf{(B)}\ 240\pi \textbf{(C)}\ 260\pi \textbf{(D)}\ 280\pi \textbf{(E)}\ 500\pi$