AMC 8 2013 Problem 25

AMC8 2013 年第 25

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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?
直径为 4 英寸的球从 A 开始沿着图示轨道滚动。轨道由 3 段半圆弧组成,半径分别为 R1=100 英寸,R2=60 英寸,R3=80 英寸。球全程都和轨道紧密接触,并且不会滑动。那么当球从 A 滚到 B,球心所经过的路程是多少英寸?
AMC 8 2013 Problem 25 figure
  1. A.238π238\pi
  2. B.240π240\pi
  3. C.260π260\pi
  4. D.280π280\pi
  5. E.500π500\pi

正确答案 · Correct Answer

A

解析 · Solution

解析整理中

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