Question

下图区域由 $24$ 个边长为 $1$ 厘米的正方形组成。能放入该区域内部、可以接触边界的最大圆的面积是多少平方厘米？

The region shown below consists of $24$ squares, each with side length $1$ centimeter. What is the area, in square centimeters, of the largest circle that can fit inside the region, possibly touching the boundaries?

$3\pi$

$4\pi$

$5\pi$

$6\pi$

$8\pi$

答案：C

知识点：圆面积勾股定理最优化

难度评级：1280

视频讲解：

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文字解答：

离区域中心最近的边界角点，是图中位于这个圆上的 $8$ 个点：

由勾股定理，每个点到中心的距离为所以圆面积为选 C。 $\sqrt{1^2 + 2^2} = \sqrt{5}.$ $\pi (\sqrt{5})^2 = 5\pi,$

The corners of the region which are closest to the center are the $8$ points which lie on this circle:

By the Pythagorean Theorem, each of these points has this distance from the center: $\sqrt{1^2 + 2^2} = \sqrt{5}.$ The area of the circle is then $\pi (\sqrt{5})^2 = 5\pi,$ which is choice C.

2025 AMC 8 第 12 题

答案：C

难度评级：1280

视频讲解：

文字解答：

其他年份的第 12 题