AMC8 2026

AMC8 2026 · Q23

AMC8 2026 · Q23. It mainly tests Circle theorems, Area & perimeter.

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?

Lakshmi 有 $5$ 个直径为 $4$ 厘米的圆形硬币。她将硬币如图所示，摆成两排放在桌面上，并用橡皮筋紧紧地围绕它们。橡皮筋的长度是多少厘米？

(A) 2\pi + 20 2\pi + 20

(B) \frac{5}{2}\pi + 20 \frac{5}{2}\pi + 20

(D) \frac{9}{2}\pi + 20 \frac{9}{2}\pi + 20

(E) 9\pi + 20 9\pi + 20

Answer

Correct choice: (C)

正确答案：（C）

Solution

In order to find the length of the elastic band, perpendicular lines are added to the figure to divide the band into sections for easier calculation. After the additions, the length of band consist of five identical lines and a full circle, the four shaded areas. The total length is five lines, the diameter of the coins, plus the circumference of a coin, so 5d+4π. Finally, the length of the elastic band is $\boxed{\textbf{(C)}4\pi+20}.$

为了求橡皮筋的长度，在图中添加了垂直线，将橡皮筋分成几个部分以便计算。添加后，橡皮筋的长度由五条相同的线段和一个完整的圆组成，即四个阴影部分。总长度是五条线段的长度加上一个硬币的周长，即 $5d + 4\pi$。最后，橡皮筋的长度是 $\boxed{\textbf{(C)}4\pi+20}$。

Topics