2. 外语
  3. The rectangular solid above is made up of eight cubes of the same size, each of which has exactly one face painted blue. What is

The rectangular solid above is made up of eight cubes of the same size, each of which has exactly one face painted blue. What is

admin2009-05-19  15
问题
The rectangular solid above is made up of eight cubes of the same size, each of which has exactly one face painted blue. What is the greatest fraction of the total surface area of the solid that could be blue?
选项 A、1/6
B、3/14
C、1/4
D、2/7
E、1/3
答案D
解析 上图所示的长方体由8块同样大小的立方体构成，每个立方体仅有一个面被涂成蓝色。问该长方体的表面是蓝色的部分占其总表面积的最大比例是多少?
解：本题的正确答案为(D)。蓝色部分占表面最大比例的情况是8个立方体的蓝色表面均露在外面，共有8个平方单位，而长方体的表面共有28个平方单位，因而蓝色部分占长方体表面积的最大比值为8/28=2/7。
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