Let $PD_{n}$ be the cone of positive definite $n \times n$ real matrices and let $B$ be the unit sphere in $n \times n$ dimensions. What is the volume of $PD_{n} \cap B$?

EDIT: Let's assume that $B$ is the unit sphere w.r.t the operator norm: $||A||=\sup_{||x||=1}{||Ax||}$.