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Approximation a cone

  • Thread starter brandy
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  • #1
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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
 

Answers and Replies

  • #2
tiny-tim
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my question: does centreing the ellipses effect the volume. im pretty sure it doesnt but i want to verify
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:
 
  • #3
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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.
 
  • #4
tiny-tim
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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.
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:
 
  • #5
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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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