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Volume help

  1. Sep 15, 2008 #1
    The attempt at a solution[/b]Question: Find the volume of the solid whose base is the triangular region of the xy-plane with vertices (0,0),(1,0),(0,1) and whose cross sections perpendicular to the y-axis are equilateral triangles.

    I have the problem set up. just don't know how to get the cross sections of the triangles. i know the area is 1/2 bh i thought maybe similar triangles where the height would be sqrt(3)/4x and x=1-y. am i close? help
     
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  3. Sep 15, 2008 #2

    Dick

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    Sure, you're close. The base is x=(1-y). The height is base*sqrt(3)/2. So what's the area?
     
  4. Sep 15, 2008 #3
    so the area is sqrt(3)/2 (1-y)^2? and i would just integrate that from 0 to 1 right?
     
  5. Sep 15, 2008 #4

    Dick

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    Almost right. The area is (1/2)*b*h. What happened to the (1/2)?
     
  6. Sep 15, 2008 #5
    ah. so its sqrt(3)/4 (1-y)^2
     
  7. Sep 15, 2008 #6

    Dick

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    Yes it is.
     
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