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Math Help - Volume bounded by cylinders (Multivar)

  1. #1
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    Volume bounded by cylinders (Multivar)

    Find the volume bounded by the cylinders x^2+y^2=r^2 and y^2+z^2=r^2.

    That's the full question, and I am confused because both of those equations would seem to form circles.
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  2. #2
    Senior Member Shanks's Avatar
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    V=\iint_{x^2+y^2\leq r^2} 2\sqrt{r^2-y^2} dxdy
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    I have no idea what that means or where it came from.
    Last edited by davesface; December 14th 2009 at 09:51 AM.
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  4. #4
    Senior Member Shanks's Avatar
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    have you learned the multiple integral part in calculus class?
    please refer to the definition, and try you best to image the solid.
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  5. #5
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    Yes, we have gone over multiple integrals and I understand that part of the notation, but little else.

    1. Where did that integrand come from?
    2. What does the x^2+y^2\leq r^2 region mean? I've looked over my past notes and there is definitely nothing like that in there.
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