1. In the square $A B C D$, construct the inscribed circle $\odot 0$, which is tangent to $A B$ at point $Q$ and to $C D$ at point $P$. Connect $P A$ and $P B$ to form the isosceles $\triangle P A B$. Rotating these three figures (the square, the circle, and the isosceles triangle) around their common axis of symmetry $P Q$ for one full revolution results in a cylinder, a sphere, and a cone. The volume ratio $V_{\text {cylinder }}$ : $V_{\text {sphere }}: V_{\text {cone }}=$
ニ、1.3:2:1.
Let the side length of the square be $2a$, then
$$
\begin{array}{l}
V_{\text {rounded }}=S h=\pi a^{2} \cdot 2 a=2 \pi a^{3} \text {, } \\
V_{\text {** }}=\frac{4}{3} \pi a^{3}, V_{\text {base }}=\frac{1}{3} S h=\frac{2}{3} \pi a^{3} \text {. } \\
\end{array}
$$

Thus, $V_{\text {rounded }}: V_{\text {** }}: V_{\text {base }}=2: \frac{4}{3}: \frac{2}{3}=3: 2: 1$.