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Thread: Need Help in Vector Calculus Multiple Integral

  1. #1
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    Cool Need Help in Vector Calculus Multiple Integral

    Use cylindrical coordinates to find the volume of the solid between two sheets of the hyperboloid z2 =64+x2+y2 bounded by the cylinder x2+y2=225. (HINT: Use symmetry and elementary geometry to simplify the calculation.)
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  2. #2
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    Re: Need Help in Vector Calculus Multiple Integral

    What help do you need? Have you converted the hyperboloid to cylindrical coordinates?
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  3. #3
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    Re: Need Help in Vector Calculus Multiple Integral

    225= 15^2 so x^2+ y^2= 225, r= 15 in cylindrical coordinates, is the cylinder with axis the z-axis and radius 15. The hyperboloid is z^2= 64+ x^2+ y^2= 64+ r^2 or z= \pm\sqrt{64+ r^2} in cylindrical coordinates. The volume of the region between the two branches of the hyperbola, inside the cylinder, is given by \int_0^{2\pi}\int_0^{15}\int_{-\sqrt{64+ r^2}}^{\sqrt{64+ r^2}} r dzdrd\theta}= 2\pi\int_0^{15}\int_{-\sqrt{64+ r^2}}^{\sqrt{64+ r^2}} r dzdr= 4\pi\int_0^{15} r\sqrt{64+ r^2}dr.
    Last edited by HallsofIvy; Nov 20th 2017 at 01:31 PM.
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    Re: Need Help in Vector Calculus Multiple Integral

    Thanks a lot!
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