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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


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    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.
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