AMC8 2003

AMC8 2003 · Q15

AMC8 2003 · Q15. It mainly tests 3D geometry (volume), Geometry misc.

A figure is constructed from unit cubes. Each cube shares at least one face with another cube. What is the minimum number of cubes needed to build a figure with the front and side views shown?

一个由单位立方体构成的图形。每个立方体至少与另一个立方体共享一面。建造一个具有所示正面和侧视图的最少需要多少个立方体？

(A) 3 3

(B) 4 4

(D) 6 6

(E) 7 7

Answer

Correct choice: (B)

正确答案：（B）

Solution

There are only two ways to construct a solid from three cubes so that each cube shares a face with at least one other: [figures]. Neither ... has both the front and side views shown. The four-cube configuration has the required front and side views. Thus at least four cubes are necessary.

只有两种方法用三个立方体构成每个立方体至少与一个其他共享一面的固体：[图形]。两者都没有所示的正面和侧视图。四立方体的配置具有所需的正面和侧视图。因此至少需要四个立方体。

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