2003 AMC 8 第 22 题
先试着解答 2003 AMC 8 第 22 题，然后核对你的答案与精心整理的解答，解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2003 AMC 8 解答，或核对答案。
所有题目均经美国数学协会（MAA）官方合法授权使用。
22.
下列图形由正方形和圆组成。哪个图形的阴影区域面积最大？
The following figures are composed of squares and circles. Which figure has a shaded region with largest area?
只有
only
只有
only
只有
only
和
both and
全部相等
all are equal
小提示：
图形 和 留下相同的阴影面积
Figures and leave the same shaded area.
大提示：
对于 ，比较 和
For compare with
解答：
在图形 中，阴影面积是一个 乘 正方形面积减去半径为 的圆面积，即 。
图形 由四个边长为图形 一半的副本组成，所以每个副本的面积是原图的四分之一，总阴影面积也为 。
在图形 中，圆的半径为 ，内接正方形的对角线为 ，所以其面积为 。阴影面积为 。
因为 ，所以 ，因此图形 的阴影面积最大。
所以正确答案是 C。
In figure the shaded area is the area of a by square minus a circle of radius so it is
Figure is made of four copies of figure with half the side length, so each copy has one-fourth the area and the total shaded area is also
In figure the circle has radius and the inscribed square has diagonal so its area is The shaded area is
Since we have so figure has the largest shaded area.
Thus, C is the correct answer.
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