Question

一个边长为 $n$ 个单位的木质立方体六个面全部涂红，然后切成 $n^3$ 个单位小立方体。所有小立方体面的总数中，正好有四分之一是红色的。 $n$ 是多少？

A wooden cube $n$ units on a side is painted red on all six faces and then cut into $n^3$ unit cubes. Exactly one-fourth of the total number of faces of the unit cubes are red. What is $n?$

$3$

$4$

$5$

$6$

$7$

答案：B

知识点：正方体表面积比与比例

难度评级：1400

解答：

小立方体共有 $6n^3$ 个面，其中来自原立方体外表面的红色面共有 $6n^2$ 个。因此 $\dfrac{6n^2}{6n^3} = \dfrac{1}{n} = \dfrac{1}{4}$ ，所以 $n = 4$ 。

所以正确答案是 B。

The unit cubes have $6n^3$ faces total, of which the original surface accounts for $6n^2$ red faces. Then $\dfrac{6n^2}{6n^3} = \dfrac{1}{n} = \dfrac{1}{4},$ so $n = 4.$

Thus, the correct answer is B.

2005 AMC 10A 第 11 题

答案：B

难度评级：1400

解答：

其他年份的第 11 题