Question

Lakshmi 有 $5$ 枚圆形硬币，每枚直径为 $4$ 厘米。她把硬币按图中 $2$ 行摆在桌上，并用一根弹性带紧紧围住它们。弹性带的长度是多少厘米？

Lakshmi has $5$ round coins of diameter $4$ centimeters. She arranges the coins in $2$ rows on a table top, as shown below, and wraps an elastic band tightly around them. In centimeters, what will be the length of the band?

$2\pi + 20$

$\dfrac{5}{2}\pi + 20$

$4\pi + 20$

$\dfrac{9}{2}\pi + 20$

$5\pi + 20$

答案：C

知识点：周长圆周长梯形

难度评级：1690

视频讲解：

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文字解答：

追踪这些硬币圆心的路径。圆心形成的凸包是一个梯形，底边为 $8$ ，上底为 $4$ ，两条斜边长度都是 $4$ ，所以周长为 $20$ 。硬币半径为 $2$ ，弹性带绕过圆角时额外增加一个完整圆周，长度为 $2\pi\cdot2=4\pi$ 。因此弹性带长度为 $20+4\pi$ 。

Trace the path of the centers of the coins. Their convex hull is a trapezoid with bottom side $8$ , top side $4$ , and two slanted sides of length $4$ , so its perimeter is $20$ . Wrapping the band around coins of radius $2$ adds one full circumference, $2\pi\cdot2=4\pi$ . The band length is $20+4\pi$ .

2026 AMC 8 第 23 题

答案：C

难度评级：1690

视频讲解：

文字解答：

其他年份的第 23 题