# 2013 AMC8 Problem 25

#### bridge

##### Member
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?

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