Question

一个长方体的每个顶点都被一刀切掉，切面穿过该顶点相邻的三条棱，在八个顶点各切去一个小三角形部分。新立体有多少条棱？

Every corner of a rectangular prism is cut off by a straight slice through the three edges meeting at that corner, removing a small triangular piece at each of the eight corners. How many edges does the new figure have?

$24$

$30$

$36$

$42$

$48$

答案：C

知识点：多面体

难度评级：1180

解答：

长方体原来有 $12$ 条棱。切掉顶点只会把这些棱截短，不会把它们完全去掉。

每个顶点切口会产生一个小三角形面，带来 $3$ 条新棱。共有 $8$ 个顶点，所以新增 $8 \cdot 3 = 24$ 条棱，总数是 $12 + 24 = 36$ 。

所以正确答案是 C。

A rectangular prism starts with $12$ edges, and cutting corners only shortens them without removing any.

Each of the $8$ corner cuts creates a small triangular face with $3$ new edges, adding $8 \cdot 3 = 24$ edges. The total is $12 + 24 = 36$ .

Thus, the correct answer is C .

1990 AMC 8 第 18 题

答案：C

难度评级：1180

解答：

其他年份的第 18 题