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Volume of a cap of a sphere

  1. Oct 24, 2007 #1
    Find the volume of a cap of a sphere with radius r and height h.
    A picture of it is given here;
    http://sjc.ilrn.com/ilrn/bca/user/appletImage?dbid=1276286560 [Broken]

    2. Relevant equations
    The area of a circle is [tex]\pi\[/tex]r^2

    3. The attempt at a solution
    So I flattened the sphere into a circle and solved me equation for x;
    Then I rotated it around the y-axis and integrated to find;
    [tex]\pi[/tex][tex]\int[/tex][tex]\stackrel{h}{r}[/tex](r²-y²)dy= [tex]\pi[/tex]((1/3)h³+(2/3)r³-hr²)

    But the computer program I do my homework on tells me that it wrong. Now I'm confused. What did I do wrong?
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Oct 24, 2007 #2


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    Science Advisor
    Homework Helper

    As h->0 the volume should go to zero, right? Does yours? That's a clue something is wrong. Look at your limits of integration again. Are they right?

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