12 Oct 13
Originally posted by CampaignerPolyhedron you mean? Hard one to answer. I'm not sure if you can quantify it as you can keep making them with a larger and larger surface area in comparison to volume. If you are talking about regular polyhedrons, then maybe there is some kind of formula to define this. If you are talking about irregular shapes then I think the possibilities are endless. Look at the small intestine or lung lining for example.
Does anyone know which shape has the most surface area in relationship to its volume (liquids) or is it a constant?
12 Oct 13
Originally posted by CampaignerA sphere.
Does anyone know which shape has the most surface area in relationship to its volume (liquids) or is it a constant?
This is why liquids in weightlessness form a sphere.
Oh, wait, you said MOST surface area.
Sorry, the sphere has the LEAST surface area in relation to its volume.
If I were to hazard a guess, I'd say a tetrahedron. It's possible the answer needs more vertices, though.
12 Oct 13
Originally posted by Sicilian SausageOoooooh, brilliant, I didn't even think of irregular surfaces.
Polyhedron you mean? Hard one to answer. I'm not sure if you can quantify it as you can keep making them with a larger and larger surface area in comparison to volume. If you are talking about regular polyhedrons, then maybe there is some kind of formula to define this. If you are talking about irregular shapes then I think the possibilities are endless. Look at the small intestine or lung lining for example.
12 Oct 13
2 edits
Yes a Sphere definitely has the lowest ratio and I would guess a tetrahedron would have the most as well. If n = the number of faces then as n tends to infinity then our shape would become a sphere. If you work back the other way it implies that the shape with the smallest number of possible faces would have the largest ratio i.e a tetrahedron.
Poink.
Or you could Google it 😀
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13 Oct 13
Originally posted by CampaignerThe answer would be a three dimensional object consisting of a surface of any shape, separated by distance d from a surface of any shape, as d approaches zero.
Does anyone know which shape has the most surface area in relationship to its volume (liquids) or is it a constant?
13 Oct 13
Originally posted by JS357Ah. I thought the OP was questioning the surface area to mass ratio of different shapes as a comparison. i.e. with a set volume for example. If you introduce size then yes, the smaller any object is, so increases said ratio, as n, d, v or whatever you want tends to 0.
The answer would be a three dimensional object consisting of a surface of any shape, separated by distance d from a surface of any shape, as d approaches zero.
