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Math Help - surface area of the torus

  1. #1
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    surface area of the torus

    Hello everybody...

    I have a problem, can help me with this??


    A torus of radius 3 (and cross-sectional radius 1) can be represented parametrically by the function

    by:
    where D is the rectangle given by .


    Help please.


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  2. #2
    Super Member Random Variable's Avatar
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    You have to integrate the length of the normal vector to the surface over the region given in the  \theta \phi plane.
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  3. #3
    Super Member Random Variable's Avatar
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    First find the tangent vectors  T_{\theta} and T_{\phi}

    In this problem, for example,  T_{\theta} = \frac {\partial \Phi}{\partial \theta} =  (-(3+cos\phi)sin \theta, (3+cos \phi)cos \theta,0)

    Then find the cross product of  T_{\theta} and T_{\phi}

    Now you have a vector normal to the surface of the torus. Find the magnitude of this vector.

    then surface area of the torus =  \int^{2 \pi}_{0} \int^{2 \pi}_{0} ||T_{\theta} \times T_{\phi}|| d \phi d \theta
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  4. #4
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    ThanKsssss You Saved My Life... !!!!!!
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