The two parallel sides of a trapezoid are $a$ and $b$, and the height is $m$. What is the volume of the solid of revolution formed by the rotation of the trapezoid around its larger parallel side?
The resulting solid of revolution consists of a cylinder and two cones. If the heights of the cones are $x$ and $y$, then:

$$
\begin{gathered}
K=m^{2} \pi b+m^{2} \pi \cdot \frac{x}{3}+m^{2} \pi \cdot \frac{y}{3}= \\
=m^{2} \pi\left(b+\frac{x+y}{3}\right)=m^{2} \pi\left(b+\frac{a-b}{3}\right)=\frac{m^{2} \pi}{3}(a+2 b)
\end{gathered}
$$

Number of solutions: 48.