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Find the mass of the surface of the triangle with the given vertices and density.

  1. Aug 2, 2012 #1

    s3a

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    1. The problem statement, all variables and given/known data
    Find the mass of the surface of the triangle with vertices (2,0,0), (0,2,0) and (0,0,1) if the density is 4xz. The solution is attached as TheSolution.jpg.

    2. Relevant equations
    Integration. Cross product. Plane equation: a(x-x_0) + b(y-y_0) + c(z-z_0) = 0 where <a,b,c> = n (vector that is normal to the plane) and where (x_0,y_0,z_0) is any arbitrarily chosen vertice.

    3. The attempt at a solution
    Having watched (1) and read (2),:

    (1)
    (2) http://www.math.oregonstate.edu/hom...usQuestStudyGuides/vcalc/surfint/surfint.html

    I have successfully reached the dS = sqrt(3/2) dA step and for the next step, I'm supposed to multiply the density by the surface area in order to get the mass of the surface but, I just don't see how I'm supposed to get the (4x – 2x^2 – 2xy) part nor do I see how the variable density, 4xz, relates to that; I'm not sure that it should relate but I feel it should.

    Could someone please help me understand the step I am stuck on?

    Any help would be greatly appreciated!
    Thanks in advance!
     

    Attached Files:

    Last edited by a moderator: Sep 25, 2014
  2. jcsd
  3. Aug 2, 2012 #2

    LCKurtz

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    You have expressed the plane as z in terms of x and y. In the integral, the z in the density formula 4xz must be replaced by its value in terms of x and y on the plane.
     
    Last edited by a moderator: Sep 25, 2014
  4. Aug 2, 2012 #3

    s3a

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    Thanks!
     
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