9. In tetrahedron $ABCD$, $\angle CAD = \angle CAB = \angle BAD = \frac{\pi}{3}$, $AB = p$, $AC = q$, $AD = r$, where $p$, $q$, and $r$ are known positive real numbers. Then the volume of this tetrahedron is
9. $\frac{\sqrt{2}}{12} p q r$

Take points $B^{\prime}, C^{\prime}$ on rays $A B, A C$ such that $A B^{\prime}=A C^{\prime}=A D=r$, then $A-B^{\prime} C^{\prime} D$ is a regular tetrahedron, whose height is $\frac{\sqrt{6}}{3} r$. It is easy to find, so $V_{A(X)}=\frac{1}{3} \cdot S_{\triangle, V x^{\circ}} \cdot \frac{\sqrt{6}}{3} r=\frac{1}{3} \cdot \frac{1}{2}$ $p q \sin 60^{\circ} \cdot \frac{\sqrt{6}}{3} r=\frac{\sqrt{2}}{12} p q r$.