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Homework Help: Volume of a sphere with a cylindrical hole

  1. Aug 30, 2015 #1
    Hello all,

    I am doing homework and have come upon this question:
    A cylindrical hole is drilled all the way through the center of a sphere (as shown in the figure below). Show that the volume of the remaining solid depends only on the length L of the hole, not on the size of the sphere.
    Screen Shot 2015-08-30 at 2.25.22 PM.png

    I think the problem should be solved using cylindrical shells, but I'm not sure how I should start it. Can anyone give me a hint?

  2. jcsd
  3. Aug 30, 2015 #2


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    If this is homework, in future, please fill out the Homework template and post it in the relevant HW forum.

    [Note: I've moved this thread to the Calculus HW forum for you.]
  4. Aug 30, 2015 #3


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    Hello dhph,

    How about if you try to find the volume of such a bead by revolving the shaded area around the x-axis ? Good chance R drops out !

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