Spin it!
I put a unit cube on the table and let its main diagonal be perpendicular to the table, so only one of the vertices touches the table. Then, I spin it really fast so that I can't see its real shape.
If I spun a regular tetrahedron, for example, I would see a cone. But in this case where I spin the cube, what is the volume of the object I see?
Assume that while I spin it, the main diagonal is always perpendicular to the table and the vertex touches the table at a fixed point.
The answer is 1.8138.
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1 solution
@X X See this
https://brilliant.org/problems/rotating-cube-2/