Surface area to volume ratio

[PolySquared]

Hi guys,

I have a question regarding the real life applications of the surface area to volume ratio theory. What animals utilise a high surface area to volume ratio in order to undertake efficient diffusion? My teacher said that tape worms flatten themselves in order to diffuse oxygen into their bodies efficiently, are there other animals that do a similar thing?

Thanks.

[Bri MT]

Some more applications:

- some organisms use villi to increase the rate of nutrient absorption
- villi, microvilli, and folding are used in the intestine for this purpose
-the lungs having multitudes of spherical alveoli (small subdivisions) for increased rate of diffusion for O2 and CO2

Edited for clarity

[DBA-144]

Some more applications:

- some organisms use villi to increase the rate of nutrient absorption
- villi, microvilli, and folding are used in the intestine for this purpose
-alveoli being spherical for increased rate of diffusion for O2 and CO2

Does spherical shape mean higher sa to v ratio or lower sa v ratio?
Thanks.

[Bri MT]

Does spherical shape mean higher sa to v ratio or lower sa v ratio?
Thanks.

Higher volume in comparison to SA. I've edited the original post for clarity as I can see how it might have given the wrong impression

[PolySquared]

Higher volume in comparison to SA. I've edited the original post for clarity as I can see how it might have given the wrong impression

If a spherical shape has a higher volume in comparison to SA wouldn't that make it less efficient at diffusion? What shapes have a higher surface area in comparison to volume?

[PhoenixxFire]

If a spherical shape has a higher volume in comparison to SA wouldn't that make it less efficient at diffusion? What shapes have a higher surface area in comparison to volume?

Hey,
Normally flattened sacs have the highest surface area to volume ratio.
The lungs however are made of bunches of alveoli sacs. Think of it like holding a bunch of grapes vs holding a bag of grapes. If you go by the external image (ie. ignore the inside of the grape bag) the bunch of grapes has a far higher surface area than the bag. In this case it’s more referring to the surface area of the lungs, not the surface area of individual alveoli sacs.

This image might help


Edit: Fixed image

[PolySquared]

Why does a flatter shape and higher surface area to volume ratio of the alveoli lead to more effective diffusion or oxygen in our lungs?

[Poet]

Why does a flatter shape and higher surface area to volume ratio of the alveoli lead to more effective diffusion or oxygen in our lungs?

Because the more surface area, the higher the potential area for gas exchange. This means that more oxygen can pass in and out of the cell because of its increased SA.

[Bri MT]

Why does a flatter shape and higher surface area to volume ratio of the alveoli lead to more effective diffusion or oxygen in our lungs?

Higher surface area -> more places for the molecules to cross over -> faster rate of cross over.

As an analogy: if you chucked everyone in your school in the gym the rate at which people went outside would be higher if the door was bigger     (people = molecules, door = membrane/surface area, volume = size of the gym)

[PolySquared]

Is there a mathematical method of predicting how changing the shape or size of an object will impact its surface area to volume ratio?

[Poet]

Sort of... generalised to the shape of a cube, the equation for the SA is SA = 6L² (where L is the length of one side of the cube), and the equation for the volume is given by V = L³
So, according to this rule, the increase in size leads to an increase in volume, but a lessening of surface area ratio-wise. Here's an example:



You can see that with a side length of 1, SA is 6 times more than the volume. With a side length of 2, however, the SA is only 3 times more than the volume, and so on...
Hope you can understand this. 

[PolySquared]

Sort of... generalised to the shape of a cube, the equation for the SA is SA = 6L² (where L is the length of one side of the cube), and the equation for the volume is given by V = L³
So, according to this rule, the increase in size leads to an increase in volume, but a lessening of surface area ratio-wise. Here's an example:

(Image removed from quote.)

You can see that with a side length of 1, SA is 6 times more than the volume. With a side length of 2, however, the SA is only 3 times more than the volume, and so on...
Hope you can understand this. 

Thank you, that makes sense. Is there any way of predicting how a change in shape impacts the SA:V ratio? For example, if a shape is stretched X amount, it leads to an X increase in its surface area relative to its volume. Also, what shape has the highest surface area relative to its volume?

[Poet]

I'm sorry, but I don't know of any mathematical value attributed to specific shapes compared to the SA:V ratio. However, I do know that many organisms use multiple folds in their cells to maximise their SA. These microvilli (right at the top of the picture), for example, fold over themselves in order to create a huge SA compared to their actual volume:



This is the most effective shape used by cells and organisms to maximise their SA. I think miniturtle mentioned this earlier.

EDIT: Also, it's just a matter of logic when you think about it; long, thin, stretched-out cells would have a higher SA:V ratio than a spherical cell because they have spread their mass, allowing for a higher exchange rate.

[PolySquared]

I'm sorry, but I don't know of any mathematical value attributed to specific shapes compared to the SA:V ratio. However, I do know that many organisms use multiple folds in their cells to maximise their SA. These microvilli (right at the top of the picture), for example, fold over themselves in order to create a huge SA compared to their actual volume:

(Image removed from quote.)

This is the most effective shape used by cells and organisms to maximise their SA.


EDIT: Also, it's just a matter of logic when you think about it; long, thin, stretched-out cells would have a higher SA:V ratio than a spherical cell because they have spread their mass, allowing for a higher exchange rate.

Thanks again for your response. Is there a general trend between the SA:V ratio and the shape? For example, if a shape is stretched then its surface area will increase at a faster rate relative to its volume because the surface area becomes proportional to the amount the shape is stretched?

[Poet]

Thanks again for your response. Is there a general trend between the SA:V ratio and the shape? For example, if a shape is stretched then its surface area will increase at a faster rate relative to its volume because the surface area becomes proportional to the amount the shape is stretched?

I'm not sure if I understand your question... I'm sure that there would be an increase in SA if you stretched it out, but no matter how far you stretch a cell of a particular size, its internal volume will remain the same.