Question

从这个 $3\text{ cm}\times 3\text{ cm}\times 3\text{ cm}$ 的立方体中去掉每个角上的小立方体。剩余图形的表面积是

Each corner cube is removed from this $3\text{ cm}\times 3\text{ cm}\times 3\text{ cm}$ cube. The surface area of the remaining figure is

$19\text{ sq.cm}$

$24\text{ sq.cm}$

$30\text{ sq.cm}$

$54\text{ sq.cm}$

$72\text{ sq.cm}$

答案：D

知识点：表面积正方体不变量

难度评级：1390

解答：

任意两个角立方体之间都有一个单位立方体隔开，所以去掉一个角不会影响其他角。

去掉一个角时，失去三个单位正方形表面，但也露出三个新的单位正方形表面。

因此去掉角立方体不改变表面积。原立方体表面积为平方厘米。 $6 \cdot 3^2 = 6 \cdot 9 = 54$

所以正确答案是 D。

Note that there is one unit cube between any pair of corner cubes, so the removal of each does not affect the others.

When we remove a corner, we are losing three unit squares. We, however, gain these back from the three faces that get uncovered.

This means that removing a corner cube does not change the surface area. The surface area of the original cube is $6 \cdot 3^2 = 6 \cdot 9 = 54$ square centimeters.

Thus, D is the correct answer.

1997 AMC 8 第 21 题

答案：D

难度评级：1390

解答：

其他年份的第 21 题