Problem E

I Want More Volume

A rectangular prism is placed on a table. Points \(P\), \(Q\), and \(R\) lie on three different faces of the prism with \(P\) on the top face and \(Q\) and \(R\) on two adjacent side faces. Each point is located where the diagonals of the particular face intersect. Connecting these three points gives us \(\triangle PQR\).

If \(PQ=4\) cm, \(QR=5\) cm, and \(RP=6\) cm, determine the volume of the rectangular prism.