What is the volume of a region in R3 bounded by a hyperboloid and two planes?

[calcer7531]

Can some one help me with the following problem? Find the volume of the region contained in R3 bounded by the hyperboloid x^2+y^2-z^2=1 and the planes z=1 and z= -1. Thank you.

 

[HallsofIvy]

That volume is infinite. You have a paraboloid of one sheet that has axis of symmetry along the z-axis. Cutting the paraboloid by any plane of the form z= constant gives an unbounded set.

 

[kakarotyjn]

integrate S*dz from -1 to 1.S=pi*(r^2)=pi*(x^2+y^2)=pi*(1+z^2)

that is integrate pi*(1+z^2)dz from -1 to 1.