Ratio between volume and area in different sized spheres

[jps001]

Trying to crack my head round this one. I have been told by others smarter than myself in terms of maths that the ratio of volume to surface area of a sphere changes when the sphere size changes. I thought, apparently incorrectly, that theoretically the ratios remained the same no matter what the size of the sphere was. So if you took three spheres and measured the ratios between volume and surface area and plotted those on a graph you'd get a curve for each ratio point. What puzzles me (without taking into consideration the limits of matter/subatomic matter) is that if it is a curve would we not end up at the end of the curve something like a sphere with no volume?

 

[mmm4444bot]

What puzzles me ... is that if it is a curve would we not end up at the end of the curve something like a sphere with no volume?

There's no such thing as a sphere with no volume.

If you reduce the radius to zero, then you've reduced the sphere to a point (called a singularity, in some contexts). Points are dimensionless. :cool:

 

[jps001]

There's no such thing as a sphere with no volume.

If you reduce the radius to zero, then you've reduced the sphere to a point (called a singularity, in some contexts). Points are dimensionless. :cool:

No, I do realise that. I wasn't proposing that such a thing exists. Still my question isn't answered though.

 

[Deleted member 4993]

Just like rectangle with no area is a line (no longer has the properties of a rectangle and is not called rectangle) - sphere without volume degenerates into a point.

For sphere:

(volume)/(surface area) = (4/3 * π * r³)/(4 * π * r²) = r/3

Now, where is the confusion?

 

[stapel]

No, I do realise that. I wasn't proposing that such a thing exists. Still my question isn't answered though.

If no such thing exists, then the question about the non-existent thing is unlikely to be answerable.

It would be like asking what food to pick up at the pet store, in case you find a unicorn waiting for you when you get home. Since unicorns don't exist (aww!), there is no answer as to which food to buy.

 

[mmm4444bot]

What puzzles me (without taking into consideration the limits of matter/subatomic matter) is that if it is a curve would we not end up at the end of the curve something like a sphere with no volume?

Let me try again.

If you follow the curve toward the origin, then the volume is getting smaller and smaller. You will never reach the origin, however, because you can continue to get closer and closer to zero without reaching it. This is because there is no such thing as "the smallest" positive number.

Radius = 0.01
Radius = 0.001
Radius = 0.0001
Radius = 0.00001
Radius = 0.000001
Radius = 0.0000001
Radius = 0.00000001
Radius = 0.000000001
Radius = 0.0000000001
Radius = 0.00000000001
Radius = 0.000000000001
Radius = 0.0000000000001
Radius = 0.00000000000001
Radius = 0.000000000000001
Radius = 0.0000000000000001
Radius = 0.00000000000000001

This pattern continues forever ...

At some point, the radius and volume of the ever-decreasing sphere become so small that there is no way to measure or even comprehend them. Yet, the sphere still exists, mathematically.

So, when you draw the graph, put an open circle at the origin, to show that the point (0,0) is not a part of the graph. :cool: