Question

一个正八面体有八个等边三角形面，每个顶点处有四个面相交。Jun 将通过折叠下面这张纸做出图中所示的正八面体。哪个编号的面最终会在阴影区域 $Q$ 的右侧？

A regular octahedron has eight equilateral triangle faces with four faces meeting at each vertex. Jun will make the regular octahedron shown in the figure by folding the piece of paper below. Which numbered face will end up to the right of the shaded region $Q?$

$1$

$2$

$3$

$4$

$5$

答案：A

知识点：展开图（立体几何）多面体

难度评级：1580

视频讲解：

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文字解答：

折叠后，编号 $2$ 、 $3$ 、 $4$ 和 $5$ 的面形成八面体的下半部分，因此只需在剩余面中考虑。

候选面是 $1$ 、 $6$ 和 $7$ 。从网格关系可看出， $6$ 会在 $Q$ 的左侧，而 $7$ 又在 $6$ 的左侧。

因此，剩下的面 $1$ 必须在 $Q$ 的右侧。

所以正确答案是 A。

Begin by observing that when folded, the sides labelled $2,$ $3,$ $4,$ and $5$ form the bottom half of the octahedron. As such, the remaining four faces must make up the top half of the octahedron.

From here, we have narrowed down our possibilities to $1,$ $6,$ and $7.$ We can see that $6$ will be the number to the left of the shaded region $Q.$ This also gives us that $7$ is to the left of $6.$

Therefore, we know that the only remaining face, $1,$ must be to the right of the shaded region $Q.$

Thus, A is the correct answer.

2023 AMC 8 第 17 题

答案：A

难度评级：1580

视频讲解：

文字解答：

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