Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Volume of a region in R3

  1. Dec 16, 2009 #1
    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.
  2. jcsd
  3. Dec 17, 2009 #2


    User Avatar
    Science Advisor

    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.
  4. Dec 17, 2009 #3
    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook