A cone with apex $P$ and base center $O$ has base radius $\sqrt { 3 }$. $PA$ and $PB$ are slant heights of the cone, $\angle A O B = 120 ^ { \circ }$. If the area of $\triangle P A B$ equals $\frac { 9 \sqrt { 3 } } { 4 }$, then the volume of the cone is\\
A. $\pi$\\
B. $\sqrt { 6 } \pi$\\
C. $3 \pi$\\
D. $3 \sqrt { 6 } \pi$