THIS MONTH'S QUIZ
1. ABCDEFGH is a wooden cube with edges of length 1 ft. The corner E is cut off with a straight sawcut as shown to expose the triangular area AFH (coloured green). Find the volume of the piece removed.
2. Three other corners, B, D and G, are removed in the same way, leaving the regular tetrahedron ACFH. Find the volume of the tetrahedron.
3. Find CP, the perpendicular distance of C from the plane AFH.
[Hint: The volume of any pyramid (and hence of any tetrahedron) is one third the area of its base multiplied by its perpendicular height.]