Something in Common 29: Volume of a Tetrahedron

Earliest recommended Year group: Year 13.

Given the 3D coordinates of four points what is the volume of the tetrahedron that is formed by joining them with line segments? This brings together just about everything they need to know about vectors and so is a good revision task. Using the triple product to solve it takes some of the fun out (hence suitable up to C4). Of course, the volumes are all the same.... but why?

This is from the “Something in Common” collection of resources by John Burke. They allow consolidation of key skills, prevent students from copying each other (as all the questions are different), make marking and assessing easy for the teacher (as all the answers are the same!), and provide a lovely extra challenge for students as they try to figure out exactly what is going on! To access the full collection, and read John’s background notes, please visit: http://www.mrbartonmaths.com/common.htm