10,11

The lateral edges of a triangular pyramid are pairwise perpendicular and equal to $a, b$, and $c$. Find the volume of the pyramid.
Let the lateral edges $D A, D B$, and $D C$ of the triangular pyramid $A B C D$ be pairwise perpendicular, and $D A=a, D B=b$, $D C=c$. Consider the triangular pyramid $A B C D$ with vertex $C$ and base $A B D$. Its lateral edge $C D$ is perpendicular to two intersecting lines $B D$ and $A D$ in the plane $A B D$. Therefore, $C D$ is a perpendicular to this plane. Thus, $C D=c$ is the height of the pyramid $A B C D$. The base of this pyramid is a right triangle $A B D$ with legs $A D=a$ and $B D=b$. Therefore,

$$
V_{A B C D}=\frac{1}{3} S_{\triangle A B D} \cdot C D=\frac{1}{3} \cdot \frac{1}{2} a b \cdot c=\frac{1}{6} a b c
$$

## Answer

$\frac{1}{6} a b c$.