# Surface Area vs Volume in Biology

1. Feb 12, 2004

### holly

Can someone pull a rabbit out of a hat for me & explain why just because an object (like a cell or an animal) gets bigger, its surface area doesn't get proportionally bigger? I made myself a little chart where I took a sphere & found the vol & the s.a. at 1 cm radius, at 2 cm radius, and 3 cm radius, then divided s.a. by the vol, the numbers were getting smaller, but can someone put it into words for me or can this only be understood mathematically? I just am not getting it intuitively...

2. Feb 12, 2004

### Loren Booda

Assume a cell to be spherical. Its surface area A equals 4(pi)r2, and its volume V equals 4(pi)r3/3, where r is its radius. The surface area varies as the square of r, and the volume more rapidly as the cube of r.

What happens to the cell surface area and the cell volume when one changes the radius? By increasing or decreasing r, the cell experiences more rapid change in volume than surface area. To see this, just calculate V/A=r/3, showing that V outgrows (or outshrinks) A by the factor r/3.

Cells with large surface area transpire more, have more osmosis and more contact with their environment in general. Cells with greater volume metabolize more, have less motility, ingest and excrete (through the membrane) more.

For a particular cell, there is an ideal V/A, or r0 value.

3. Feb 12, 2004

### holly

Thank you, now it is clearer to me...a bit clearer...the more stuffing in the cell, the less material to cover such a large amount of stuffing...the less stuffing in the cell, the more material...proportionally speaking? I wonder why most cells are not flatter? Thank you again.

4. Feb 12, 2004

### Monique

Staff Emeritus
Prokaryotic cells are small for that reason, they don't have internal membranes and thus have to depend on their plasma membrane for processes to occur.

Eukaryotic cells are much larger, they can be that because of the internal organelles and thus extra membranes that they have. Also, transportation systems have evolved in the cell where a molecule can hitch a ride on a structure like the subway.

5. Feb 13, 2004

### iansmith

Staff Emeritus
How would you explain this?

http://en.wikipedia.org/wiki/Thiomargarita_namibiensis
http://www.bacteriamuseum.org/species/thiomargarita.shtml

The discover a giant bacteria few years ago. It is called Thiomargarita namibiensis. There is another one from a surgeonfish guts called Epulopiscium fishelsoni.

6. Feb 13, 2004

### Monique

Staff Emeritus
maybe they elvolved organelles? just a guess
I'll look at the links later :)

7. Feb 13, 2004

### iansmith

Staff Emeritus
Epulopiscium fishelsoni has membrane folding so the surface area is increased.

Thiomargarita namibiensis has a fluid-filled vacuole that represent 98% of the volume and it is use to store nitrate which oxidize sulfur.

8. Feb 13, 2004

### holly

Thanks for the help...as concerns the size of the cell dictating when it will divide, being that if it gets to a non-optimal size for the s.a./vol ratio, why, instead of dividing into two daughter cells (which I realize would then have a better s.a/vol ratio as concerns getting nutrients needed for its size), why, then, don't the membranes just begin indenting...getting lots of microvilli maybe? Then the volume inside can be supported better...why pinching into two with all the effort that takes with mitosis and so forth?

9. Feb 13, 2004

### Monique

Staff Emeritus
Vacuoles, plants use those a lot to increase cell size without compromising cellular function. Ever looked at onion membrane under a microscope? The cytoplasm is a very very thin layer against the plasma membrane, the rest is all a water filled vacuole :)

10. Feb 13, 2004

### LURCH

Is there a point during the cell's developement when vacuoles begin to form, or are they present from the beginning of its existence?

11. Feb 14, 2004

### Monique

Staff Emeritus
Good question.. we can't make our organelles de novo, we need an existing organelle to make more. I guess the same holds true for vacuoles, but just maybe they can evolve from the other vesicles.

The function of vacuoles is starch storage or other nutrients. In the plant it creates the turgor needed to grow. If you don't give a plant water, the vacuoles will become smaller and the plant will wilt.

12. Feb 14, 2004

### eagleone

|plants|: They are present from the begging of cells life. Almost all plant cells originate from meristem cells (I’m afraid I don’t know proper English term for it-I’m thinking on apical and basal, let’s say, stem cells), which have many small vacuoles that they transfer to offspring (daughter cells).

But plant cells (in contrast to animal) have powerful ability to transform from cells of one to another tissue, with almost no limits (except death), but as I remember vacuole is always there …