6. On the edge $A C$ of the triangular pyramid $A B C D$, there is a point $M$ such that $A M: M C=3: 4$. Through the midpoint of the edge $B C$ of the base of the pyramid, a plane $P$ is drawn passing through point $M$ and parallel to the lateral edge $C D$. In what ratio does the plane $P$ divide the volume of the pyramid?
Answer: $V_{1}: V_{2}=22: 27$

## National Research Nuclear University "MEPhI" Final round of the sectoral physics and mathematics olympiad for schoolchildren "Rosatom", mathematics, field trip 11th grade.