Question 121
Let $ABCD A'B'C'D'$ be a rectangular parallelepiped, where $ABCD$ is the bottom face with the vertices labelled clockwise, and $A, B, C$, and $D$ lie below $A', B', C'$, and $D'$ respectively. The parallelepiped is divided into eight pieces by three mutually orthogonal planes parallel to the faces of the parallelepiped. For each vertex $P$ of the parallelepiped, let $V_P$ denote the volume of the piece of the parallelepiped that contains $P$. Given that $V_A=40$, $V_C=300$, $V_{B'}=360$ and $V_{C'}=90$, what is the volume of the parallelepiped $ABCD A'B'C'D'$?