1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Volume generated

  1. Mar 22, 2010 #1
    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?
    Last edited: Mar 22, 2010
  2. jcsd
  3. Mar 22, 2010 #2


    User Avatar

    Re: Volume generated[Solved]

    It looks like you are integrating z^2 instead of z. Also shouldn't there be an extra r in the integral?

    ie. [tex]\int\int z*r dr d\vartheta[/tex] whereas it looks like you are doing [tex]\int\int z^2 dr d\vartheta[/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook