Volume generated[Solved] Use polar coordinates to find the volume of the given solid enclosed by the hyperboloid -x2-y2+z2=1 and the plane z=2. I wrote out the integral [tex]\int\int 1+r^2 dr d\vartheta[/tex] integrated from 0 to [tex]2\pi[/tex] and r integrated from 0 to sqrt3 and volume enclosed gotten to be [tex]15\pi[/tex]/2. So this is the volume enclosed by the hyperboloid and the xy-plane correct? So I wanted to use the volume of the cyclinder to subtract off the volume found previously. But the volume is [tex]6\pi[/tex] so if I subtract i would get negative volume?