Question

六个棱长为一英寸的立方体如图固定在一起。求总表面积，单位为平方英寸。包括顶面、底面和侧面。

Six cubes, each an inch on an edge, are fastened together, as shown. Find the total surface area in square inches. Include the top, bottom, and sides.

$18$

$24$

$26$

$30$

$36$

答案：C

知识点：表面积立体几何

难度评级：1550

解答：

可以数不暴露的面，从而求出有多少个面贡献表面积。

有三个立方体各有 $1$ 个面不暴露，两个立方体各有 $2$ 个面不暴露，一个立方体有 $3$ 个面不暴露。

不暴露面总数为 $3 \cdot 1 + 2 \cdot 2 + 1 \cdot 3 = 10$ 。因此暴露面数为 $6 \cdot 6 - 10 = 36 - 10$ $= 26$ 。

每个暴露面贡献的面积为 $1^2 = 1$ ，所以总表面积为 $1 \cdot 26 = 26.$

所以正确答案是 C。

We can count the number of unexposed sides to find how many sides contribute to the surface area.

Three cubes have $1$ side unexposed, two cubes have $2$ sides unexposed, and one cube has $3$ sides unexposed.

This gives us a total of $3 \cdot 1 + 2 \cdot 2 + 1 \cdot 3 = 10$ unexposed sides, which gives us $6 \cdot 6 - 10 = 36 - 10$ $= 26$ exposed sides.

Each exposed side contributes $1^2 = 1$ to the surface area, for a total surface area of $1 \cdot 26 = 26.$

Thus, C is the correct answer.

2002 AMC 8 第 22 题

答案：C

难度评级：1550

解答：

其他年份的第 22 题