Question

一个立方体有八个顶点和十二条棱。连接两个不由一条棱相连的顶点的线段，如 $x$ ，称为对角线。线段 $y$ 也是对角线。一个立方体有多少条对角线？

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?

$6$

$8$

$12$

$14$

$16$

答案：E

知识点：正方体对角线

难度评级：1270

解答：

每个面有两条对角线，连接这个面上两对相对顶点。

另外，对于每个顶点，都有一个与它在立方体内部相对的顶点。

这样空间对角线共有 $8 \div 2 = 4$ 条。

总对角线数为 $6 \cdot 2 + 4 = 12 + 4 = 16.$

所以正确答案是 E。

Each face has two diagonals connecting each of the two pairs of opposite vertices.

Also, for each vertex, there is one corresponding vertex that lies opposite it on the cube.

There are then $8 \div 2 = 4$ interior space diagonals in the cube.

The total number of diagonals is then $6 \cdot 2 + 4 = 12 + 4 = 16.$

Thus, E is the correct answer.

1997 AMC 8 第 17 题

答案：E

难度评级：1270

解答：

其他年份的第 17 题