AMC8 1997
AMC8 1997 · Q17
AMC8 1997 · Q17. It mainly tests Basic counting (rules of product/sum), 3D geometry (volume).
A cube has eight vertices (corners) and twelve edges. A segment, such as x, which joins two vertices not joined by an edge is called a diagonal. Segment y is also a diagonal. How many diagonals does a cube have?
一个立方体有八个顶点（角）和十二条边。连接两个不相邻顶点的线段（如 x）称为对角线。线段 y 也是对角线。立方体有几个对角线？
(A)
6
6
(B)
8
8
(C)
12
12
(D)
14
14
(E)
16
16
Answer
Correct choice: (E)
正确答案：（E）
Solution
Answer (E): There are two diagonals, such as $x$, in each of the six faces for a total of twelve face diagonals. There are also four space diagonals, such as $y$, which are within the cube. This makes a total of 16.
答案（E）：立方体的每个面上有两条对角线，例如 $x$。六个面一共有 12 条面内对角线。立方体内部还有 4 条空间对角线，例如 $y$。因此总共有 16 条对角线。
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