AMC8 2003
AMC8 2003 · Q13
AMC8 2003 · Q13. It mainly tests 3D geometry (volume), Geometry misc.
Fourteen white cubes are put together to form the figure on the right. The complete surface of the figure, including the bottom, is painted red. The figure is then separated into individual cubes. How many of the individual cubes have exactly four red faces?
14 个白色小立方体组合成右图所示的图形。图形的整个表面（包括底部）被涂成红色。然后图形被拆分成单个小立方体。有多少个单个小立方体正好有四个红色面？
(A)
4
4
(B)
6
6
(C)
8
8
(D)
10
10
(E)
12
12
Answer
Correct choice: (B)
正确答案：（B）
Solution
A cube has four red faces if it is attached to exactly two other cubes. The four top cubes are each attached to only one other cube, so they have five red faces. The four bottom corner cubes are each attached to three others, so they have three red faces. The remaining six each have four red faces.
一个小立方体有四个红色面，当且仅当它只与正好两个其他立方体相连。四个顶部立方体每个只与一个其他立方体相连，所以有五个红色面。四个底部角立方体每个与三个其他相连，所以有三个红色面。其余的六个各有四个红色面。
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