Math problem
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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?
A = 238 pi
B = 240 pi
C = 260 pi
D = 280 pi
E = 500 pi -
@The-Blade-Dancer This looks very familiar.. is it an AMC 8 question?
It looks like you need to adjust the radii, since the center of the ball is 2 inches off from the edge of the ball, which follows the track. So \(R_1 = 98, R_2 = 62, \text{ and } R_3 = 78.\) Then find the circumferences of these semi-circular paths. -
AMC 8 2013 Problem 25
I remember doing this.
