One for the scientists, please explain ...

[^woody^]

Consider a plastic bottle, filled with water.

It is squeezed and a some water comes out. The internal volume is reduced.

And yet the [internal] surface area of the bottle is not reduced - it is not stretched or contracted, the same amount of plastic skin should be able to contain the same volume, and yet it does not.

So why is this?

 

[tim west]

if you leave the lid on the water doesnt come out

 

[Shutpa]

should be able to contain the same volume, and yet it does not.

So why is this?

Surely it can if you replace the water that squirted out!

 

[Trazor]

Imagine the bottle being flattened by a car, still the same amount of internal surface area, but its volume is considerably decreased.

The largest volume for a known internal surface area, would be a perfect sphere.

 

[^woody^]

Also, consider a piece of string on a flat desk.

Join the two ends together, and then whatever shape you make, the internal area will always be the same.

So, using this principle for the internal area of the bottle, then why does volume change if the area of the material containing the volume does not change?

Yes, obviously squash the bottle up and it will hold nothing, but again the internal surface area has not changed, so why can it not hold the same volume?

 

[ColJack]

the volume of the bottle is reduced

think of a cube..

6 sides of say 10x10cm..

that's a surface area of 600cm² ( 10 x 10 x 6 )yes?

that holds a volume of 1000cm³ (10 x 10 x 10 )

now consider an oblong with 2 oposing sides of 15 x 15cm.. which gives a surface area of 450cm² leaving 150 to make up to the 600cm² that we require.

the other 4 sides are therefore 15x2.5cm..

which gives a volume of.. 15 x 15 x 2.5 = 562.5m³

eventually you can get to an internal surface areaof 600cm² with no gap between sides.. and therefore no internal volume.. ( it's 20 x 15cm in case you were interested )

 

[Trazor]

Also, consider a piece of string on a flat desk.
Join the two ends together, and then whatever shape you make, the internal area will always be the same.

No, if you make a circle, that will be the largest area possible.

If you put 2 pencils inside your loop, and pull apart, the area will be considerably reduced.

 

[ricicle]

Join the two ends together, and then whatever shape you make, the internal area will always be the same.

Not true. Consider a piece 40cm long joined. It could make a 10cmx10cm square (100cm²) or a rectangle 2cmx18cm (36cm²)

 

[mikeyd]

Suppose your string on the table is 8 inches long, and you make a square with it, the area is 2x2=4. You could also make a rectangle 3x1 and the area will then be 3. So the area isn't the same for different shapes. The same applies to your bottle. As stated above the shape with the most volume for a given surface area is a sphere. That's why bubbles take a spherical shape.

 

[ColJack]

Also, consider a piece of string on a flat desk.

Join the two ends together, and then whatever shape you make, the internal area will always be the same.

no it won't..

a piece of string 40cm in length..

with that you make a square 10 x 10 cm.. ( 4 sides of 10cm ) this is an area of 100cm²

same piece of string now make it a rectangle of 15 x 5 ( still equals 40cm ) this makes an area of 75cm²

EDIT: bah! too slow...

 

[Thermo]

what if the bottle and the string are on a conveyour belt?

 

[ColJack]

lol

 

[tim west]

Now you're talking!

 

[^woody^]

OK, the string was probably a bad example, but the principle is the same - why doesn't the same perimeter contain the same area?

 

[bhm1712]

its all about the surface area to volume ratio