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Finding volume/mass of 3D Solid

  1. Apr 3, 2013 #1
    1. The problem statement, all variables and given/known data

    The volume shown lies above a square in the (x, y) plane having corners (4, 1), (5, 1), (5, 2), and (4, 2). The remaining two surfaces are planes defined by z1 = 2x + 4y + 7 and z2 = 3x + 6y + 8. The density of this object is 880.y. Determine a) the volume of this object, and b) the mass of this object.

    A picture is attached

    2. Relevant equations

    I can't use the coding on here, so bear with me:

    Volume of a 3D object is given by V=∫∫∫dxdydz

    Mass of a 3D object is: m=∫∫∫ρdxdydx
    where ρ is the density


    3. The attempt at a solution

    My setup for the volume is:

    ∫∫∫dzdxdy
    Limits of integration:
    2x+4y+7 < z < 3x + 6y + 8.
    4<x<5
    1<y<2

    And for mass:

    ∫∫∫800y dzdxdy

    with the same limits of integration

    I've gotten 8.5 and 10333.3 for the volume and mass, respectively, but those are wrong.

    Can anyone see what I'm doing wrong?
     

    Attached Files:

  2. jcsd
  3. Apr 3, 2013 #2

    LCKurtz

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    Gold Member

    Your work looks correct to me. I get the same answers as you.
     
  4. Apr 3, 2013 #3
    AH I see what I did wrong. When I calculated the mass I used density = 800y instead of 880y
     
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