How do you work out the volume of a cuboid if only given the areas of the faces of a cuboid?

Answer 1

If the areas of the three faces are x, y and z then the volume is sqrt(x*y*z).

Proof:

Suppose the sides of the cuboid are a, b and c.

Then the different areas of the faces are ab, bc and ca.

If these are called x, y and z, then x*y*z = ab*bc*ca = (a*b*c)^2

and that, as yuo will notice, is the square of the volume.