A pyramid with a square base and sides that are equilateral triangles contains a cube. If the cube is taking maximum space as shown, what is the fraction of its volume to the pyramid’s volume?
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The King’s chamber

A pyramid with a square base and sides that are equilateral triangles contains a cube. If the cube is taking maximum space as shown, what is the fraction of its volume to the pyramid’s volume?
On two faces of a cube a diagonal is drawn that meet in the same vertex. What’s the angle between them?