1991 AMC 8 第 15 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。
15.
一个长方体的六个面都是长方形。如图，从这个长方体中切去一个边长为一英尺的立方体。新立体的表面积比原立体的表面积多或少多少平方英尺？
All six sides of a rectangular solid were rectangles. A one-foot cube was cut out of the rectangular solid as shown. The total number of square feet in the surface of the new solid is how many more or less than that of the original solid?
少
less
少
less
相同
the same
多
more
多
more
小提示：
切掉立方体会去掉一些原本在表面的面，也会露出一些新的面；比较这两个面积
Cutting the cube removes some faces that were on the surface but uncovers new ones; compare the two amounts
大提示：
被切掉的小立方体的上、前、后三个面原本在表面上，去掉 平方英尺；凹口的底面和两个侧壁成为新表面，又增加 平方英尺
The cube’s top, front, and back faces were on the surface ( square feet removed); the notch’s floor and its two side walls become new surface ( square feet added)
解答：
被切掉的小立方体有三个面原来在立体表面上：上面、前面、后面，所以移除了 平方英尺表面积。
切出凹口后，又露出三个新面：凹口底面和两个侧壁，共增加 平方英尺。因此表面积不变。
所以正确答案是 C。
The removed cube had three faces on the surface of the solid (top, front, and back), so square feet of surface are removed.
Cutting it out exposes three new faces (the floor of the notch and its two side walls), adding square feet. The surface area is unchanged.
Thus, the correct answer is C .
其他年份的第 15 题
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