Question

一个立方体的棱长为 $2$ 。现在把一个棱长为 $1$ 的立方体粘在大立方体的上方，使它的一个面完全贴在大立方体的上表面上。从原立方体到新形成的立体，其表面积（侧面、顶面和底面）的百分比增加最接近

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

$10$

$15$

$17$

$21$

$25$

答案：C

知识点：表面积百分数

难度评级：1510

解答：

原来的表面积为 $6 \cdot 2^2 = 6 \cdot 4 = 24.$

注意单位立方体的顶面加上大立方体顶面仍可见的部分，面积与大立方体一个面相同。

因此放在上方的单位立方体只让总表面积增加 $4$ 个单位正方形，增加量为 $4$ 。

百分比增加为 $100 \cdot \dfrac{4}{24} = 100 \cdot \dfrac{1}{6} \approx 16.7\%.$

所以正确答案是 C。

The original surface area is just $6 \cdot 2^2 = 6 \cdot 4 = 24.$

Note that the top face of the unit cube plus the visible area of the top face of the larger cube is the same as the area of one face of the larger cube.

This means that the unit square on top only adds $4$ unit squares to the total surface area, making the increase $4.$

The percent increase is therefore $100 \cdot \dfrac{4}{24} = 100 \cdot \dfrac{1}{6} \approx 16.7\%.$

Thus, C is the correct answer.

2000 AMC 8 第 22 题

答案：C

难度评级：1510

解答：

其他年份的第 22 题