2005 AMC 12A Problem 17

A unit cube is cut twice to form three triangular prisms, two of which are congruent, as shown in Figure 1. The cube is then cut in the same manner along the dashed lines shown in Figure 2. This creates nine pieces. What is the volume of the piece that contains vertex W?

\textbf{(A) } \frac{1}{12} \qquad \textbf{(B) } \frac{1}{9} \qquad \textbf{(C) } \frac{1}{8} \qquad \textbf{(D) } \frac{1}{6} \qquad \textbf{(E) } \frac{1}{4}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.