Question

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?

$2\pi + 20$

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

$4\pi + 20$

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

$5\pi + 20$

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Written solution:

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 Problem 23

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Problem 23 in Other Years