7. If the distance from the center $O$ of $\odot O$ to the line $l$ in the plane where $\odot O$ lies is $d$, and the radius of the circle is $r(d>r>0)$, then the volume of the torus (tire) obtained by rotating $\odot O$ around the line $l$ once is $\qquad$
7. $2 \pi^{2} r^{2} d$

Construct a cylinder with a base radius of $r$ and a height of $4 \pi d$.
Take one quarter of the cylinder, flip it over, and then take half of the torus, and use a plane at a distance $h$ from the base to cut these two geometric bodies. The cross-sectional area of the torus is
$$
S=\pi\left(r_{2}^{2}-r_{1}^{2}\right)=4 \pi d \sqrt{r^{2}-h^{2}},
$$

where $r_{2}=d+\sqrt{r^{2}-h^{2}}, r_{1}=d-\sqrt{r^{2}-h^{2}}$;
The cross-sectional area of the quarter cylinder is
$$
S=4 \pi d \sqrt{r^{2}-h^{2}}.
$$

Using the principle of Zu Chongzhi, the volume of the torus is
$$
V=\frac{1}{2} V_{\text {torus}}=\frac{1}{2} \pi r^{2} \times 4 \pi d=2 \pi^{2} r^{2} d .
$$