AMC 8 2018 Problem 24

AMC8 2018 年第 24

立体几何★★★★
In the cube ABCDEFGHABCDEFGH with opposite vertices CC and EE, JJ and II are the midpoints of edges \overlineFB\overlineFB and \overlineHD\overlineHD, respectively. Let RR be the ratio of the area of the cross-section EJCIEJCI to the area of one of the faces of the cube. What is R2R^2?
在正方体 ABCDEFGHABCDEFGH 中,顶点 CCEE 相对,点 JJ 和点 II 分别是棱 \overlineFB\overlineFB\overlineHD\overlineHD 的中点。RR 表示横截面 EJCIEJCI 的面积和正方体的一个面的面积之比,求 R2R^2
AMC 8 2018 Problem 24 figure
  1. A.54\displaystyle \frac{5}{4}
  2. B.43\displaystyle \frac{4}{3}
  3. C.32\displaystyle \frac{3}{2}
  4. D.2516\displaystyle \frac{25}{16}
  5. E.94\displaystyle \frac{9}{4}

正确答案 · Correct Answer

C

解析 · Solution

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