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Homework Help: Area of revolution of hyperbola

  1. Feb 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the hyperbola y2−x2=4 and the lines y=0, x=3 and x=5 about the y− axis.

    2. Relevant equations

    Nothing specific...general equations

    3. The attempt at a solution

    So I would write it as
    I was wondering if it was just 2x*pi*dx*(√4+x2) from x=3 and x=5? Or would I have to incorporate the "hole" from x=0 to x=3.
  2. jcsd
  3. Feb 12, 2010 #2


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    Hi ~Sam~! :smile:

    (have a pi: π :wink:)

    Yes, just ∫35 2x*π*dx*√(4+x2) …

    you're "adding" the volumes of the cylindrical shells that make up the whole shape, so you only need the shells with radii from 3 to 5. :smile:
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