Approximating a Cone: Find Volume, Centering Effects & Linear Lines

[brandy]

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. I am pretty sure it doesn't 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

 

[tiny-tim]

my question: does centreing the ellipses effect the volume. I am pretty sure it doesn't but i want to verify

Hi brandy!

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.

 

[brandy]

i don't 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 don't form a perfect elliptical cone.

 

[tiny-tim]

i don't 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 don't 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. ​

 

[brandy]

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.