Schrödinger's cat and Math

Cube diagonal intersection point on the cube face containing the vertex has a octahedron.
It is you cat?
When the length of the cube diagonal is A, volume of octahedron?
Is you a dead cat?
You did not.

This question is Korea middle third year student second semester midterm examination 5 points.
This problem is difficult enough to Schrödinger's cat.
But the answer comes clear.