8. In a right trapezoid, the upper base is shorter than the lower base. If the volume of the solid of revolution obtained by rotating it around its lower base is $80 \pi$,

the volume of the solid of revolution obtained by rotating it around its upper base is $112 \pi$, and the volume of the solid of revolution obtained by rotating it around its right leg is $156 \pi$, then the perimeter of the right trapezoid is
Solution: Let the length of the upper base be $a$, the length of the lower base be $b$, and the height be $h$, then we have $\pi h^{2} a+\frac{1}{3} \pi h^{2}(b-a)=80 \pi$,
$$
\begin{array}{l}
\pi h^{2} b+\frac{1}{3} \pi h^{2}(b-a)=112 \pi, \\
\frac{1}{3} \pi\left(a^{2}+a b+b^{2}\right) h=156 \pi,
\end{array}
$$

Solving these equations, we get $a=3, b=9, h=4$, thus the length of the non-perpendicular side is $2 \sqrt{13}$, and the perimeter of the right trapezoid is $16+2 \sqrt{13}$.