AMC10 2003 A
AMC10 2003 A · Q10
AMC10 2003 A · Q10. It mainly tests 3D geometry (volume).
The polygon enclosed by the solid lines in the figure consists of 4 congruent squares joined edge-to-edge. One more congruent square is attached to an edge at one of the nine positions indicated. How many of the nine resulting polygons can be folded to form a cube with one face missing?
图中实线围成的多边形由 4 个全等的正方形边对边连接而成。再在 9 个指示位置之一的边上附加一个全等的正方形。其中 9 个结果多边形有多少个可以折叠成缺一面立方体？
(A)
2
2
(B)
3
3
(C)
4
4
(D)
5
5
(E)
6
6
Answer
Correct choice: (E)
正确答案：（E）
Solution
(E) If the polygon is folded before the fifth square is attached, then edges $a$ and $a'$ must be joined, as must $b$ and $b'$. The fifth face of the cube can be attached at any of the six remaining edges.
（E）如果在连接第五个正方形之前先把多边形折起来，那么边 $a$ 和 $a'$ 必须相接，边 $b$ 和 $b'$ 也必须相接。立方体的第五个面可以连接在剩下的六条边中的任意一条上。
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