AMC 8 2000 Problem 22
AMC8 2000 年第 22 题
立体几何★★★☆☆
A cube has edge length 2 . Suppose that we glue a cube of edge length 1 on top of the big cube so that one of its faces rests entirely on the top face of the larger cube. The percent increase in the surface area (sides, top, and bottom) from the original cube to the new solid formed is closest to
一个正方体边长为 2。假设我们把一个边长为 1 的正方体粘贴到这个大的正方体的顶面，使得小正方体的一个面整个的放在大正方体的顶面上。则和原来大正方体的表面积（侧面，顶面，底面）相比较，所形成的新的立体图形的表面积增加的百分数最接近于百分之多少？
- A.10
- B.15
- C.17
- D.21
- E.25
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
The original cube has 6 faces, each with an area of square units. Thus the original figure had a total surface area of 24 square units. The new figure has the original surface, with 6 new faces that each have an area of 1 square unit, for a total of 6 additional square units. But 1 square unit of the top of the bigger cube, and 1 square unit on the bottom of the smaller cube, is not on the surface, and does not count towards the surface area. The total surface area is therefore 24 + 6 - 1 - 1 = 28 square units. The percent increase in surface area is , giving the closest answer as .
To be honest, we could just bash this one out to get about 20%, which is C. Yaaaay! BRO, who ever made this is tweaking, if you bashed it to 20 you would choose D so this is not bashable. Tsk Tsk Plus they never said how to bash¯_(ツ)
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