A 3D object is suspended in the air and it casts shadows on each orthogonal plane. The shadows are in the form of a circle, triangle and square, as shown in the diagram below. What is the shape of the mystery object?
Assuming the object we seek is solid all the way through (in the same way as a cube, tetrahedron or sphere would be), this mystery object can be created by...
...intersecting a cylinder with a triangular prism.
The resulting object looks like this:
(Images taken from missouristate.edu).
The circular shadow is formed by shining a light directly along the cylindrical component, the triangular shadow is formed by light hitting the end of the triangular prism head-on, and the square shadow is formed by light hitting the triangular prism from the side.
A nice image showing the shadow effect in action can be seen here:
Namely that this is not the only object that satisfies this property, and others with smaller volumes can be constructed - for instance, by laying a horizontal circular base board and positioning two intersecting vertical boards - one triangular and one square - on top.