Problem:
A ball with diameter inches starts at point to roll along the track shown. The track is comprised of semicircular arcs whose radii are inches, inches, and inches, respectively. The ball always remains in contact with the track and does not slip. What is the distance in inches the center of the ball travels over the course from to
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Solution:
The diameter of the ball is inches, so its radius is inches. The center of the ball rolls through semicircles of radii inches, inches, and inches, respectively. The length of the path is then inches.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions