AMC 8 2002 Problem 22
AMC8 2002 年第 22 题
立体几何★★★☆☆
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.
如下图所示，6 个边长为 1 的正方体被粘在一起。请求出这个立体的总表面积，包含顶面，底面和侧面（单位：平方英寸）。
- A.18
- B.24
- C.26
- D.30
- E.36
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
Count the number of sides that are not exposed, where a cube is connected to another cube and subtract it from the total number of faces. There are 5 places with two adjacent cubes, covering 10 sides, and (6)(6)=36 faces. The exposed surface area is .
We can count the number of showing faces from each side. One thing that we notice is that the front face has the same number of squares as the back face, the side faces have the same surface area, etc. Therefore, we are looking for . We find that this is . Solution by ILoveMath31415926535
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