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?

- Joined
- 06 Apr '08
- Moves
- 62206

- Joined
- 14 Jul '07
- Moves
- 43012

USA- Joined
- 16 Feb '08
- Moves
- 88320

Dumnonia- Joined
- 21 Aug '04
- Moves
- 55993

In your face12 Oct '13 19:19

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.*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?**- Joined
- 08 Aug '03
- Moves
- 35774

Isle of Misfit Toys12 Oct '13 20:01

A sphere.*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?**

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.- Joined
- 08 Aug '03
- Moves
- 35774

Isle of Misfit Toys12 Oct '13 20:04

Ooooooh, brilliant, I didn't even think of irregular surfaces.*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.**- Joined
- 21 Aug '04
- Moves
- 55993

In your face12 Oct '13 20:212 editsYes 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˜€- Joined
- 29 Dec '08
- Moves
- 6788

13 Oct '13 06:06

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.*Originally posted by Campaigner*- Joined
- 16 Aug '05
- Moves
- 76863

Wat?- Joined
- 21 Aug '04
- Moves
- 55993

In your face13 Oct '13 09:43

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.*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.**- Joined
- 09 Jun '07
- Moves
- 45641

at home- Joined
- 09 Jun '07
- Moves
- 45641

at home- Joined
- 06 Apr '08
- Moves
- 62206

- Joined
- 06 Apr '08
- Moves
- 62206