The radius of the base of a right circular cylinder is $r$. We cut this cylinder with a plane not parallel to the base, such that the shortest side of the remaining cylinder is $a$, and the longest side is $b$. What is the volume of this obliquely cut cylinder and the area of its lateral surface $\mathrm{s}$?
$$
V=r^{2} \pi \frac{a+b}{2}, P=r \pi(a+b) .
$$

Number of solutions: 30.