2013 AMC8 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?
\( \textbf{(A)}\ 238\pi\\\textbf{(B)}\ 240\pi\\\textbf{(C)}\ 260\pi\\\textbf{(D)}\ 280\pi\\\textbf{(E)}\ 500\pi \)