AMC 8 2014 Problem 19

AMC8 2014 年第 19

立体几何★★★☆☆
A cube with 3-inch edges is to be constructed from 27 smaller cubes with 1-inch edges. Twenty-one of the cubes are colored red and 6 are colored white. If the 3-inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white?
一个边长为 3 英寸的大正方体是由 27 个边长为 1 英寸的小正方体组成的。其中 21 个小正方体是红色的,6 个是白色的。若要求大的正方体的表面积中白色部分越少越好,那么表面积的白色部分所占总表面积的比例是多少?
  1. A.554\displaystyle \frac{5}{54}
  2. B.19\displaystyle \frac{1}{9}
  3. C.527\displaystyle \frac{5}{27}
  4. D.29\displaystyle \frac{2}{9}
  5. E.13\displaystyle \frac{1}{3}

正确答案 · Correct Answer

A

解析 · Solution

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