Question 38
On the cube $A B C D E F G H$, denote the centre of the face $E F G H$ by $P$ and the midpoint of the edge $A B$ by $R$. The plane $\Sigma$ containing the points $C, P$ and $R$ intersects the edges $E F$ and $G H$ at the points $X$ and $Y$, respectively.
a) Prove that $|E X|:|X F|=|G Y|:|Y H|=1: 3$.
b) The plane $\Sigma$ divides the cube into two parts.
Determine the ratio of the volumes of these two parts.
a) Prove that $|E X|:|X F|=|G Y|:|Y H|=1: 3$.
b) The plane $\Sigma$ divides the cube into two parts.
Determine the ratio of the volumes of these two parts.