AMC8 1991

AMC8 1991 · Q15

AMC8 1991 · Q15. It mainly tests 3D geometry (surface area), Geometry misc.

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?

一个长方体所有六个面都是矩形。从长方体中按图示切出一个一英尺的立方体。新长方体表面的总平方英尺数比原长方体的表面积多多少或少多少？

(A) 2 less 少2

(B) 1 less 少1

(D) 1 more 多1

(E) 2 more 多2

Answer

Correct choice: (C)

正确答案：（C）

Solution

When the one-foot cube is removed, three square feet of surface area are “removed”, but three new square feet of surface area are “uncovered”. Thus the original surface area is unchanged.

移除一英尺立方体时，“移除”了三平方英尺表面积，但“暴露”了三平方英尺新表面积。因此原表面积不变。

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