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Volume of solid region

  1. Oct 22, 2006 #1
    so i have one problem and i just need to know if my integral is right. any help would be greatly appreciated

    1. a ball of radius 10 has a round hole of radius 5 drilled through its center. find the volume of the resulting solid.

    i know volume of cylinder removed is pi*5^2*10*sqrt(3)

    because h^2/4 + 5^2=10^2 so h = sqrt(300)= 10*sqrt(3)

    and i know the volume of original sphere is 4/3*pi*10^3

    and now what?
    i think i need to do integral of pi*(100-y^2) dy from 10 to 10*sqrt(3) and multiply this whole answer by 2
    is that right?

    if so what do i do with these three pieces of information?

    thank you!!!
    Last edited: Oct 23, 2006
  2. jcsd
  3. Oct 24, 2006 #2


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    I advise you to be meticulous in setting up the limits of integration.
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