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Math Help - What's wrong in my answer to this question? (About find volumes of solids)

  1. #1
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    What's wrong in my answer to this question? (About find volumes of solids)

    Ok, guys.

    I am on my first year on Engineering Mechanics and by now I got stuck at this problem:

    A hole of radius r is bored through the center of a sphere of
    radius R > r . Find the volume of the remaining portion of the
    sphere.


    The reason is that my answer doesn't match with the book's one.

    OK, here is what I did:

    A picture worths more than 1000 words




    I know another way to solve it, and it gives me the right answer. But I can't find any gap at the answer I did above


    Thank you for you atention, and Math bless you all.
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  2. #2
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    Quote Originally Posted by AmaymonF View Post
    Ok, guys.

    I am on my first year on Engineering Mechanics and by now I got stuck at this problem:

    A hole of radius r is bored through the center of a sphere of
    radius R > r . Find the volume of the remaining portion of the
    sphere.


    The reason is that my answer doesn't match with the book's one.

    OK, here is what I did:

    A picture worths more than 1000 words




    I know another way to solve it, and it gives me the right answer. But I can't find any gap at the answer I did above


    Thank you for you atention, and Math bless you all.


    I can't understand what you wrote above: it is too dim and scarcely explained, but check the following which

    is the usual mistake of many in this particular problem: the bored hole through the sphere is not a straight

    cylinder but one with both top and basis "rounded".

    I think I guess this is what you missed when you wrote the formula for A(x) ...

    Tonio
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  3. #3
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    EUREKA!!!

    Oh yeah, man. You enlighted me. I cannot integrate from 0 to R but from 0 to sqrt(R^2 - r^2).
    Thank youuu =D
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