Volume of torus

I wanna calculate the volume of a torus that is created when the circlearea $(x-4{)}^{2}+{y}^{2}\le 4$ revolves around the y-axis. I don't understand what the difference would be if I calculated the volume of the circle $(x-4{)}^{2}+{y}^{2}=4$ revolving around the y-axis. Doesn't the circlearea just create a solid torus instead of a hollow? Then comes the practical problem of finding a formula for the volume. My idea is that if the distance from the "right" and "left" side of the circle to origo is R and r respectively, then the area of the thin circles that constitute the torus is $\pi ({R}^{2}-{r}^{2})$. Then the height is dy and so we integrate from, if x denotes the radius of the circle, -r to r. Would this work?

I wanna calculate the volume of a torus that is created when the circlearea $(x-4{)}^{2}+{y}^{2}\le 4$ revolves around the y-axis. I don't understand what the difference would be if I calculated the volume of the circle $(x-4{)}^{2}+{y}^{2}=4$ revolving around the y-axis. Doesn't the circlearea just create a solid torus instead of a hollow? Then comes the practical problem of finding a formula for the volume. My idea is that if the distance from the "right" and "left" side of the circle to origo is R and r respectively, then the area of the thin circles that constitute the torus is $\pi ({R}^{2}-{r}^{2})$. Then the height is dy and so we integrate from, if x denotes the radius of the circle, -r to r. Would this work?