AMC 8 1985 Problem 11
AMC8 1985 年第 11 题
立体几何★★★☆☆
A piece of paper containing six joined squares labeled as shown in the diagram is folded along the edges of the squares to form a cube. The label of the face opposite the face labeled is
一张纸上有六个相连的正方形，标记如图所示。将纸沿正方形的边折叠形成一个正方体。与面 相对的面上的标记是
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
Notice that two faces of a cube are opposite each other if and only if they share no vertices. The diagram shows that shares at least one vertex with each of , , , and , so by process of elimination must be opposite .
To find the face opposite , we can find the faces sharing an edge with , so the only face remaining will be the opposite face.
Clearly, and share an edge with . Also, the faces , , and share a common vertex, therefore shares an edge with . Similarly, the faces , , and share a common vertex, so shares an edge with .
The only face doesn't share an edge with is , which is choice
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