Why do this problem?

It provides good eperience of visualisation in 3D and using ideas of similarity and scaling in 2D and 3D. They will need the formula for the volume of a tetrahedron.

It is not necesary to use 3D coordinates but they can be useful.

Possible approach

Emphasise the value of trying to visualise the plane cutting the cube. Suggesthe students close there eyes and try to visualise where the plane cuts the vertical line through $A$.

Suggest students look for similar triangles and similar 3D shapes.

Key question

Where does the line $EH$ cut the plane $PDQ$? Call this point $R$.

Where do the lines $PQ$ and $DR$ meet?