AMC 12 2005a 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 $W$?

Image:2005 AMC 12A Problem 17.png

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