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Thread: Triple integrals to find volume of sphere without cylinder inside

  1. #1
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    Triple integrals to find volume of sphere without cylinder inside

    Hello,

    Today, my teacher said that you have to use triple integrals to find the volume of sphere, minus a cylinder inside (x2 + y = 1, x2 + y2 + z2= 2), and you can't simply subtract the volumes because it doesn't take into account the "edge points." I understand how to do that in and of itself, but why can't you use subtraction of the volume of the individual figures? What does "edge points" mean?

    Thanks.
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  2. #2
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    Re: Triple integrals to find volume of sphere without cylinder inside

    Your teacher is wrong. Astoundingly so. To suggest that one dimensional circles, the intersection between the sphere and the cylinder, have volume beggars belief.
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  3. #3
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    Re: Triple integrals to find volume of sphere without cylinder inside

    Are you only subtracting the volume of the cylinder, or the volume of the cylinder and the upper and lower "dishes" as well?
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    Re: Triple integrals to find volume of sphere without cylinder inside

    Okay, several days later, the problem came up again. Turns out that my teacher simply meant that because the problem involved a cylindrical hole bored straight through the sphere, one has to also subtract the volume of the upper and lower caps/dishes in addition to the volume of the cylinder itself (which I already knew). It was simply his terminology ("edge points") to refer to those caps/dishes that confused me.
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