In the figure shown, the points labeled *X* are the midpoints of the segments with endpoints *A* and *B*.
The *X*'s all lie in a plane (the hexagon in the figure) and that plane divides the cube into two pieces of
equal volume.

If instead the *X*'s are chosen so that *AX*/*AB* = λ, determine what fraction of the
volume of the cube lies on the same side of the plane containing the *X*'s as the vertex that is
adjacent to the points labeled *A*. For example when λ = 1/2, we are in our original situation
and the fraction is 1/2. When λ = 0, the fraction is 1/6 (the corresponding piece of the cube
being a pyramid).