Age 16 to 18 Challenge Level:
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
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
Where does the line $EH$ cut the plane $PDQ$? Call this point
Where do the lines $PQ$ and $DR$ meet?