# Area v Volume

Campaigner
General 12 Oct '13 18:42
1. 12 Oct '13 18:42
Does anyone know which shape has the most surface area in relationship to its volume (liquids) or is it a constant?
2. Grampy Bobby
12 Oct '13 18:45
Originally posted by Campaigner
Does anyone know which shape has the most surface area in relationship to its volume (liquids) or is it a constant?
The RHP Science Forum "Scientific discussion and debate." would seem to be the place to post your question.
3. 12 Oct '13 18:53
Originally posted by Campaigner
Does anyone know which shape has the most surface area in relationship to its volume (liquids) or is it a constant?
Sorry no, but I do know which poster has the greatest amounts of words relative to their content, if that is any help?
4. 12 Oct '13 19:19
Originally posted by Campaigner
Does anyone know which shape has the most surface area in relationship to its volume (liquids) or is it a constant?
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.
5. Suzianne
Misfit Queen
12 Oct '13 20:01
Originally posted by Campaigner
Does anyone know which shape has the most surface area in relationship to its volume (liquids) or is it a constant?
A sphere.

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.
6. Suzianne
Misfit Queen
12 Oct '13 20:04
Originally posted by Sicilian Sausage
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.
Ooooooh, brilliant, I didn't even think of irregular surfaces.
7. 12 Oct '13 20:212 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 ðŸ˜€
8. 13 Oct '13 06:06
Originally posted by Campaigner
Does anyone know which shape has the most surface area in relationship to its volume (liquids) or is it a constant?
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.
9. 13 Oct '13 06:16
Point singularity, of course!

-m.
10. 13 Oct '13 09:43
Originally posted by JS357
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.
Ah. 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.
11. wolfgang59
Mr. Wolf
15 Oct '13 22:14
Originally posted by Campaigner
Does anyone know which shape has the most surface area in relationship to its volume (liquids) or is it a constant?
Yes.
Quite a few people.
12. wolfgang59
Mr. Wolf
15 Oct '13 22:15
Google "Menger Sponge" if you want to join them.
13. 15 Oct '13 22:34
Thanks for these answers - yes I should have mentioned it is a set volume (water in this case) - if a sphere is both the most and the least doesn't that make it a constant?
14. 15 Oct '13 22:38
Brilliant! - more or less just what I was after.