If you think about it for a bit you'll release that most cells are small: in fact too small to be seen by the unaided eye. The average cell in our body is about 50 micrometers(0.05mm) in diameter. Indeed, if you were to average the diameter of all the cells on the planet, the average would certainly be far less than that because most of the cells on this planet are bacteria and the average bacterial cell is 3-5 micrometers in diameter.

Why most cells are small has to do with simple geometry
more than anything else: specifically the relationship between surface
area to volume as a cell gets bigger. First, as a cell gets larger, the
volume of the cell increases more rapidly than the the surface area if
the cell maintains its same shape. Thus following the diagram, imagine
a cell that's a cube 1mm on a side. Its volume is 1mm^{3} and its
surface area is 6mm^{2}. But suppose the cell grows to 2mm on a
side. Now its volume is 8mm^{3} and the surface area 24mm^{2}.
The volume has increased eightfold but the surface area has increased only
four fold. It turns out that in general, the surface area increases in
proportion to the square of the width and volume as the cube of the width.
See that geometry class did come in useful!

What does this have to do with the size of cells? Everything that the cell needs or has to get rid of has to go through the cell membrane, the amount of which relates to the surface area. Therefore, the cell's ability to either get substances from the outside or eliminate waste is related to the surface area. Secondly, how much food and other material from the outside and how much waste the cell has to get rid of, is related to the volume.

Therefore, as a cell gets bigger there will come a time when its surface area is insufficient to meet the demands of the cell's volume and the cell stops growing.

There are ways to get around this problem. Bird eggs and frog eggs are much larger than typical cells, but they have a store house of food and also rapidly divide to give rize to multicelled embryos. In fact this multicellular embryo is a good illustration of another way cells get around the surface area to volume problem: they divide. In the third part of the diagram I've taken the 2mm width "cell" and divided it's volume into eight 1mm width cells. Notice that the surface area is much higher, giving more surface for obtaining nutrients, gas exchange, etc.

Another way to get around limitations of surface area is to make the
cell long and thin or skinny and flat. Notice when I make the cell thin,
even though I keep the volume 8mm^{3}, the cell's surface area
becomes 133mm^{2}, a vast increase. This technique is used by many
protists as well as certain cells in your body such as nerve cells and
muscle cells, both of which are long and skinny.

One thing this problem illustrates is that living things are shaped by basic mathemetical principles in that the types of adaptations that arise through evolution are constrined in many cases by basic geometry!

referring links:**VBS Home page,
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