## Task 2 - 150932

For a triangle $A B C$, let the side lengths $B C=a$ and the height $A D=h_{a}$ be known. A line $g$ runs such that $B C$ lies on $g$.

Calculate the volume $V$ of the body described by the rotation of the triangular area around the line $g$!
Through the planar cut with the plane that is perpendicular to $g$ and passes through $A$ (and in which the foot of the perpendicular $D$ also lies by construction), the solid of revolution is divided into two right circular cones: Both have the circle formed by the rotation of the segment $A D$ as their common base and $B$ or $C$ as their apex. Thus,

$$
V=\frac{1}{3} \cdot \pi \cdot h_{a}^{2} \cdot(|B D|+|D C|)=\frac{1}{3} \cdot \pi \cdot h_{a}^{2} \cdot a
$$