The four faces of a right triangular pyramid are equilateral triangles whose edge measures $3$ dm. Suppose the pyramid is hollow, resting on one of its faces at a horizontal surface (see attached figure) and that there is $2$ dm$^3$ of water inside. Determine the height that the liquid reaches inside the pyramid.
Problem
Source: OLCOMA Costa Rica National Olympiad, Final Round, 2018 3.6
Tags: geometry, 3D geometry, pyramid