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Approximation a cone

  1. Apr 28, 2009 #1
    you are given a contour map of a hill from which you are to approximate a cone and hence find volume.
    each contour is an ellipse

    my question: does centreing the ellipses effect the volume. im pretty sure it doesnt but i want to verify

    also. if i created 4 linear lines from the centered contour map, could i find the volume of the cone and how.

    or if you have a better idea of how to approximate a cone that would help.
    please and thankyou
     
  2. jcsd
  3. Apr 28, 2009 #2

    tiny-tim

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    Hi brandy! :smile:

    That's right: the volume of a cone depends only on the height and the cross-section-area …

    it doesn't matter whether the cone is "upright", you can move the vertex around without changing the volume, so long as you keep it at the same height. :wink:
     
  4. Apr 28, 2009 #3
    i dont think u get what i mean.
    i have 6 ellipses separated by 5 metres in height. they get progressivly smaller (as it is a hill) and they are not centred, (ie the origin is not the same for all the ellipses).
    even when they are centred they dont form a perfect elliptical cone.
     
  5. Apr 29, 2009 #4

    tiny-tim

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    That's what I thought …

    I don't think you're fully grasping the concept of "approximation" …

    of course they won't form a perfect elliptical cone … that's what an approximation is …

    but you can slide the horizontal "slices" around without changing the total volume.

    In other words: centreing the ellipses does not affect the volume. :wink:
     
  6. Apr 29, 2009 #5
    its just the upright thing sort of threw me.
    i thought you were saying that the volume is dependant on the orientation of the shape (grade 3 or 4 maths)
    but on retrospect, if i was that dumb and wasnt sure of that, why would i be approximating the volume of a cone, this is at least grade 9 maths.
    ok. thanks.
     
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