AMC 8 2009 Problem 25

AMC8 2009 年第 25

立体几何★★★★
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 1/2 foot from the top face. The second cut is 1/3 foot below the first cut, and the third cut is 1/17 foot below the second cut. From the top to the bottom the pieces are labeled A, B, C, and D. The pieces are then glued together end to end as shown in the second diagram. What is the total surface area of this solid in square feet?
一个 1 立方英尺的正方体被平行于立方体顶面的三个切口切成四块。第一个切口距离顶面英尺。第二个切口比第一个切口低英尺,第三个切口比第二个切口低英尺。从上到下,切出的这 4 块立体图形被标记为 A、B、C 和 D。接着这 4 块立体图形被一个接一个地粘合在一起, 如第二张图所示。那么新形成的立体图形的总表面积是多少平方英尺?
  1. A.\:6
  2. B.\:7
  3. C.41951\displaystyle \:\frac{419}{51}
  4. D.15817\displaystyle \:\frac{158}{17}
  5. E.\:11

正确答案 · Correct Answer

E

解析 · Solution

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