Squares of side length 1, 1, 2, 3, and 5 are arranged to form the rectangle shown below. A curve is drawn by inscribing a quarter circle in each square and joining the quarter circles in order, from shortest to longest. What is the length of the curve ?

A. $4\pi$

B. $\frac{11}{2}\pi$

C. $6\pi$

D. $8\pi$

E. $\frac{17}{2}\pi$

1. 2026 AMC 8 官方解析

方法一：长度$= \frac{1}{4} \times 2\pi \times (1 + 1 + 2 + 3 + 5) = 6\pi$ .
方法二：$C = 2\pi r$
$C_1 = 2 \times \pi \times 5 \times \frac{1}{4} = \frac{5}{2}\pi$
$C_2 = 2 \times \pi imes 3 \times \frac{1}{4} = \frac{3}{2}\pi$
$C_3 = 2 \times \pi imes 2 imes \frac{1}{4} = \pi$
$C_4 : 2 \times \pi imes 1 \times \frac{1}{4} = \frac{1}{2}\pi$
$\pi + \pi + \frac{3}{2}\pi + \frac{5}{2}\pi = 6\pi$