11. Given a point $P$ in space, the distances from $P$ to three mutually perpendicular rays $O A, O B, O C$ are $\sqrt{3}, 2, \sqrt{5}$, and the feet of the perpendiculars are $A^{\prime}, B^{\prime}, C^{\prime}$, respectively. Then the volume of the tetrahedron $P-A^{\prime} B^{\prime} C^{\prime}$ is ( ).
(A) $\sqrt{5}$
(B) $\frac{\sqrt{6}}{2}$
(C) $\sqrt{3}$
(D) $\frac{\sqrt{6}}{3}$
11. D.

Let the lengths of $O A^{\prime} 、 O B^{\prime} 、 O C^{\prime}$ be $a 、 b 、 c$. Then
$$
\begin{array}{l}
a^{2}+b^{2}=5, b^{2}+c^{2}=3, c^{2}+a^{2}=4 \\
\Rightarrow a^{2}=3, b^{2}=2, c^{2}=1 .
\end{array}
$$

By volume segmentation, we get $V_{\text {E }}=a b c$, then
$$
V_{P-A^{\prime} B^{\prime} C}=a b c-\frac{4}{6} a b c=\frac{1}{3} a b c=\frac{\sqrt{6}}{3} .
$$