2000 Fermat Problem 25

The given cube is cut into four pieces by two planes. The first plane is parallel to face ABCD and passes through the midpoint of edge BG. The second plane passes through the midpoints of edges AB, AD, HE, and GH. Determine the ratio of the volumes of the smallest and largest of the four pieces.

\textbf{(A)}\ 3{:}8\quad \textbf{(B)}\ 7{:}24\quad \textbf{(C)}\ 7{:}25\quad \textbf{(D)}\ 7{:}17\quad \textbf{(E)}\ 5{:}11

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