AHSME 1973 Problem 32

The volume of a pyramid whose base is an equilateral triangle of side length 6 and whose other edges are each of length $\sqrt{15}$ is $\textbf{(A)}\ 9 \textbf{(B)}\ 9/2 \textbf{(C)}\ 27/2 \textbf{(D)}\ \frac{9\sqrt3}{2} \textbf{(E)}\ \text{none of these}$