Question

一个棱长为 $3$ 英寸的立方体由 $27$ 个棱长为 $1$ 英寸的小立方体组成。其中十九个小立方体是白色，八个是黑色。如果八个黑色小立方体放在大立方体的八个角上，那么大立方体表面积中白色部分占几分之几？

A cube with $3$ -inch edges is made using $27$ cubes with $1$ -inch edges. Nineteen of the smaller cubes are white and eight are black. If the eight black cubes are placed at the corners of the larger cube, what fraction of the surface area of the larger cube is white?

$\dfrac{1}{9}$

$\dfrac{1}{4}$

$\dfrac{4}{9}$

$\dfrac{5}{9}$

$\dfrac{19}{27}$

答案：D

知识点：正方体表面积分数

难度评级：1390

解答：

因为每个面的黑白表面积比例相同，只需分析一个面的白色比例。

一个面上有 $9$ 个单位正方形，其中 $4$ 个是黑色。因此每个面有 $\dfrac{5}{9}$ 是白色。

所以正确答案是 D。

Since each face has the same black and white surface area, we can analyze what fraction of one side is white.

On one side, there are $9$ unit squares. $4$ of them are black. This means that $\dfrac{5}{9}$ of each face is white.

Thus, D is the correct answer.

2006 AMC 8 第 18 题

答案：D

难度评级：1390

解答：

其他年份的第 18 题