32. (MON 3) Determine the volume of the body obtained by cutting the ball of radius $R$ by the trihedron with vertex in the center of that ball if its dihedral angles are $\alpha, \beta, \gamma$.
32. Let us denote by $V$ the volume of the given body, and by $V_{0}, V_{b}, V_{0}$ the volumes of the parts of the given ball that lie inside the dihedra of the given trihedron. It holds that $V_{a}=2 R^{3} \alpha / 3, V_{b}=2 R^{3} B / 3$. $V_{c}=2 R^{3} \gamma / 3$. It is easy to see that $2\left(V_{a}+V_{b}+V_{c}\right)=4 V+4 \pi R^{3} / 3$, from which it follows that
$$
V=\frac{1}{3} R^{3}(\alpha+\beta+\gamma-\pi)
$$