2009 AMC 8 第 25 题
先试着解答 2009 AMC 8 第 25 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2009 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
25.
一个体积为一立方英尺的立方体被三次平行于顶面的切割分成四块。第一刀距离顶面 英尺。第二刀在第一刀下方 英尺处，第三刀在第二刀下方 英尺处。从上到下四块标为 、、、。然后按 、、、 的顺序首尾相接粘在一起，形成如图所示的长立体。这个立体的总表面积是多少平方英尺？
A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cut is foot from the top face. The second cut is foot below the first cut, and the third cut is foot below the second cut. From the top to the bottom the pieces are labeled and The pieces are then glued together end to end in the order to make a long solid as shown. What is the total surface area of this solid in square feet?
小提示：
从六个方向观察来思考表面积
Think of surface area by looking from the six directions.
大提示：
从任一侧面看，这四块会叠回一个单位立方体的侧视图
The four pieces stack back to a unit cube when viewed from either side.
解答：
从六个坐标方向观察这个立体。
从任一端观察时，外露竖直面的总高度等于 块的厚度，即 英尺。因此每个端向视图的面积为 平方英尺。
从每个侧面看，四块拼成原单位立方体的侧视图，所以每个侧视图面积为 平方英尺。
从上方和下方看，每个视图都显示四个 乘 的面，所以每个面积为 平方英尺。
总表面积为 平方英尺。
所以正确答案是 E。
Look at the solid from the six coordinate directions.
Viewed from either end, the exposed vertical faces have total height equal to the thickness of piece namely foot. Thus each end view has area square foot.
From each side, the four pieces stack to the side view of the original unit cube, so each side view has area square foot.
From the top and bottom, each view shows four -by- faces, so each has area square feet.
The total surface area is square feet.
Thus, E is the correct answer.
其他年份的第 25 题
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