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2026 AMC 10A Problem 19

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2026 AMC 10A Problem 19AMC 10 Step by Step

Name: Date: November 10, 2026

Solid Geometry · difficulty 4 of 5 · about 9 min · position P16-20

Three $2$ x $2$ x $2$ cubes sit on a table so that two of the cubes share a face, and a face of the third cube is centered along a shared edge of the other two cubes, as (not) shown.

A hemispherical cover is placed over the cubes so that its circumference rests on the table and the cubes are under the cover. What is the least possible value of the radius of the cover?

A) $3$
B) $\frac{\sqrt{357}}{6}$
C) $\frac{\sqrt{681}}{8}$
D) $\frac{\sqrt{178}}{4}$
E) $2\sqrt{3}$

2026 AMC 10A Problem 19

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