8、A container is already full of water. There are three lead balls: large, medium, and small. The first time, the small ball is submerged in the water; the second time, the small ball is taken out and the medium ball is submerged in the water; the third time, the medium ball is taken out and the large ball is submerged. It is known that the water overflowed the first time is 3 times that of the second time, and the water overflowed the third time is 3 times that of the first time. Find the volume ratio of the three balls $\qquad$
[Answer] $3: 4: 13$
[Solution] Let the volume of the small ball be $x$, the volume of the medium ball be $y$, and the volume of the large ball be $z$.
(1) Since the small ball is submerged in water for the first time, the volume of water overflowed for the first time is $x$.
(2) Since the small ball is taken out and the medium ball is submerged in water for the second time, the volume of water overflowed for the second time is $y-x$.
(3) Since the medium ball is taken out and the large ball is submerged in water for the third time, the volume of water overflowed for the third time is $z-y$.
According to the given conditions, we can set up the system of equations $\left\{\begin{array}{l}x=3(y-x) \\ z-y=3 x\end{array} \Rightarrow\left\{\begin{array}{l}4 x=3 y \\ z=3 x+y\end{array} \Rightarrow\left\{\begin{array}{l}y=\frac{4}{3} x \\ z=3 x+\frac{4}{3} x=\frac{13}{3} x\end{array}\right.\right.\right.$ . Therefore,
the volume ratio of the three balls is $x: y: z=x: \frac{4}{3} x: \frac{13}{3} x=3: 4: 13$.