MathDB

The bases of a right hexagonal prism are regular hexagons of side length

s > 0

, and the prism has height

h

. The prism contains some water, and when it is placed on a flat surface with a hexagonal face on the bottom, the water has depth

\frac{s\sqrt3}{4}

. The water depth doesn’t change when the prism is turned so that a rectangular face is on the bottom. Compute

\frac{h}{s}

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