2026 AMC 8 Problem 11

Below is the video solution and professionally curated solution for Problem 11 of the 2026 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2026 AMC 8 solutions, or check the answer key.

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Concepts:arc circumference

Difficulty rating: 1120

11.

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?

$4\pi$

$6\pi$

$\dfrac{13}{2}\pi$

$8\pi$

$13\pi$

Video solution:

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Written solution:

Each piece of the curve is a quarter circle. The radii are $1,1,2,3,5$ , so the total length is $\frac14\cdot2\pi(1+1+2+3+5)=\frac{\pi}{2}\cdot12=6\pi$ .

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