CEMC Hypatia, 2009

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

The prism $ABCDEF$ in part (a) is sliced with a straight cut through points $M$ , $N$ , $P$ , and $Q$ on edges $DE$ , $DF$ , $CB$ , and $CA$ , respectively. If $DM = 4$ , $DN = 2$ , and $CQ = 8$ , determine the volume of the solid $QPCDMN$ .

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