AMC8 2023

AMC8 2023 · Q17

AMC8 2023 · Q17. It mainly tests 3D geometry (volume).

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

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 将通过折叠左边所示的纸张来制作右边所示的正八面体。哪个编号的面最终会位于 $Q$ 的右侧？

(A) \ 1 \ 1

(B) \ 2 \ 2

(D) \ 4 \ 4

(E) \ 5 \ 5

Answer

Correct choice: (A)

正确答案：（A）

Solution

We color face $6$ red and face $5$ yellow. Note that from the octahedron, face $5$ and face $?$ do not share anything in common. From the net, face $5$ shares at least one vertex with all other faces except face $1,$ which is shown in green: Therefore, the answer is $\boxed{\textbf{(A)}\ 1}.$

我们将面 $6$ 涂成红色，面 $5$ 涂成黄色。注意，从八面体来看，面 $5$ 和面 $? $ 没有任何共同部分。从展开图来看，面 $5$ 与除了面 $1$（显示为绿色）以外的所有其他面至少共享一个顶点：因此，答案是 $\boxed{\textbf{(A)}\ 1}.$

Topics

GE.013 3D geometry (volume)