Integrating over or under this object

There is clearly a kink in my understanding of double integrals with polar coordinates.

Our problem is to find the volume enclosed by the hyperboloid $-{x}^{2}-{y}^{2}+{z}^{2}=1$ and plane $z=2$. I correctly figure the bounds to be $D=\{(r,\theta )|0\le \theta \le 2\pi ,0\le r\le \sqrt{3}\}.$

But I have trouble finding if we are integrating between the section of the hyperboloid and the disk $r=1$ at $z=0$ or $z=2$.

While $r\sqrt{1-{r}^{2}}drd\theta $ would make some sense as an integrand, I essentially dont know if I am integrating (ie, finding volume) under or over the surface of the hyperboloid.

There is clearly a kink in my understanding of double integrals with polar coordinates.

Our problem is to find the volume enclosed by the hyperboloid $-{x}^{2}-{y}^{2}+{z}^{2}=1$ and plane $z=2$. I correctly figure the bounds to be $D=\{(r,\theta )|0\le \theta \le 2\pi ,0\le r\le \sqrt{3}\}.$

But I have trouble finding if we are integrating between the section of the hyperboloid and the disk $r=1$ at $z=0$ or $z=2$.

While $r\sqrt{1-{r}^{2}}drd\theta $ would make some sense as an integrand, I essentially dont know if I am integrating (ie, finding volume) under or over the surface of the hyperboloid.