MathDB
SMT 2019 Geometry #5 prism

Source:

August 8, 2023
geometry3D geometryprism

Problem Statement

The bases of a right hexagonal prism are regular hexagons of side length s>0s > 0, and the prism has height hh. 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 s34\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 hs\frac{h}{s}.