Why are cells so small?

Hi,
ever wondered why you have to use microscope to see cell? Well cells are small but why?

There is a simple geometrical reason for it and it has to do with volume and surface area. First let’s take the case of cell being very big and what it would mean for it.

Such a cell would have much greater volume because of greater diameter, that is quite logical, but if you compare it to the surface area (which also increased) the ratio between the two attributes increased, meaning surface area did not grow so much as volume.

Volume (no matter the shape) grows rapidly with the function d^3 where d is the diameter [1]. On the other hand, the surface area only with d^2. So, what this means for the cell is that the surface = the membranes, are going to need to work extra hard to feed and clean up the rest of the big cell. This has some limit and that is why cells tend to be rather small and only viewable with microscope.

If the diameter is 1 than both volume and area are 1. (ratio 1/1=1)
If the diameter is 3 than volume is 27 and area 9. (ratio 27/9=3)
If the diameter is 5 than volume is 125 and area 25 (ratio 125/5=5)

The cell also cannot be too small otherwise the “equipment” (organelles) would not fit in.

Dragallur

Source: https://www.youtube.com/watch?v=wuXSEOKNxN8

[1] Take a cube for example the equation for its volume is V=a^3 where a is the side.

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