1989 AMC 8 第 23 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
23.
一位艺术家有 个边长为 米的正方体。她把它们放在地面上，搭成如图所示的雕塑，然后给雕塑露出的表面上漆。她一共要漆多少平方米？
An artist has cubes, each with an edge of meter. She stands them on the ground to form a sculpture as shown. She then paints the exposed surface of the sculpture. How many square meters does she paint?
小提示：
分别数四个竖直侧面的露出面积，再加上从上方看到的面积
Count the exposed faces on the four vertical sides, then the faces seen from directly above
大提示：
每个侧面看到的阶梯面积是 ，上表面的投影覆盖整个 底面
Each of the four sides shows exposed faces, and looking straight down covers the full footprint of top faces
解答：
因为每一层都靠齐在同一个角上，所以从每个竖直方向看，露出的阶梯侧面都是 个小正方形面，四个方向共 个侧面。
从上方看，露出的顶面覆盖整个 的底面投影，所以顶面积是 平方米。底面不漆，因此总上漆面积是 平方米。
所以正确答案是 C。
Because each higher layer is flush into one corner, each of the four vertical sides shows a stepped profile of exposed square faces, for side faces.
Viewed from directly above, the top faces cover the full footprint, adding more faces. The bottom rests on the ground and is not painted, so the total is square meters.
Thus, the correct answer is C .
其他年份的第 23 题
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- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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