AMC10 2013 A

AMC10 2013 A · Q14

AMC10 2013 A · Q14. It mainly tests Basic counting (rules of product/sum), 3D geometry (volume).

A solid cube of side length 1 is removed from each corner of a solid cube of side length 3. How many edges does the remaining solid have?

从边长为3的实心立方体每个角上切掉一个边长为1的实心立方体。剩余实心体有多少条边？

(A) 36 36

(B) 60 60

(D) 84 84

(E) 108 108

Answer

Correct choice: (D)

正确答案：（D）

Solution

The large cube has 12 edges, and a portion of each edge remains after the 8 small cubes are removed. All of the 12 edges of each small cube are also edges of the new solid, except for the 3 edges that meet at a vertex of the large cube. Thus the new solid has a total of $12 + 8(12 - 3) = 84$ edges.

大立方体有12条边，切掉8个小立方体后，每条边仍剩一部分。每个小立方体的12条边都是新实心体的边，除了在大立方体顶点相交的3条边。因此新实心体总共有$12 + 8(12 - 3) = 84$条边。

Topics