The most compact shape to give the
lowest surface area/volume ratio is a sphere, but that's not
very practical for the working of many specialised cells, tissues or
organs - but very good for single-celled organisms!
However, systems in living
organisms that involve transfer of substances, do need as large a
surface area as possible within the volume the 'system'
occupies.
To this end, many organs have
evolved to give the maximum surface area as possible
within the volume the 'system' occupies.
A bit of area/volume maths to
illustrate this idea with cubes of various sizes (6 faces):
A 1 cm cube has a volume
of 1 cm3 (1 x 1 x 1), a total surface are of 6 x 1 x 1 = 6 cm2
So the surface area / volume
ratio = 6 / 1 = 6.0 cm-1
(6 :
1 ratio)
A 2 cm cube has a volume
of 8 cm3 (2 x 2 x 2), a total surface are of 6 x 2 x 2 = 24 cm2
So the surface area / volume
ratio = 24 / 8 = 3.0 cm-1
(3 :
1 ratio)
A 3 cm cube has a volume
of 27 cm3 (3 x 3 x 3), a total surface are of 6 x 3 x 3 = 54 cm2
So the surface area / volume
ratio = 54 / 27 = 2.0 cm-1
(2 :
1 ratio)
A 4 cm cube has a
volume of 64 cm3 (4 x 4 x 4), a total surface area of
6 x 4 x 4 = 96 cm2
So the surface area /
volume ratio = 96 / 54 =
1.5 cm-1
(1.5
: 1 ratio)
You can see clearly that
the smaller (thinner etc.) the 'system' or parts of the 'system'
the greater the surface to volume ratio - potentially increasing
the rate of transfer of substances.
Good examples of this are the
millions of tiny air sacs (alveoli) in the lungs and the thin
multi-layered sections of gills in fishes - both of which are to
do with animal respiration.
Another good example is the fine and
numerous villi in the intestine where their large surface
area is very efficient for absorbing nutrients from absorbed food.
The villi can be
envisaged as tall thin rectangular blocks in shape to
maximise surface area.
An extra calculation
based on a volume of 8 units. to make the point about
villi.
A 2 x 2 x 2 block
has a surface to volume ratio of 3 : 1 (see above).
A 1 x 2 x 4 block
has a surface area to volume ratio of 3.5 : 1 (see
adaptations)
0.1 x 0.1 x 800 block has
a surface area of (2 x 0.12) + (4 x 0.1 x 800) =
0.02 + 320 = 320.02 = ~320 (3 sf)
This gives a surface to
volume ratio of 320 / 8 =
40
: 1, much higher than the blocks above,
over 10 x higher in fact.
Just think about the very
fine capillaries in the blood system too.
In any surface area : volume
calculations, make sure all measurements and calculations are
quoted with the same length units!
This is the mathematics behind
why for small cells
in single or multicellular organisms, the transfer of nutrients,
oxygen and waste products, diffusion rates are high - substances can
be moved quickly in and out of cells.
As the volume of a cell
increases, the distance from the outer cell membrane through the
cytoplasm to the centre of the cell increases.
This slows down the rate of
exchange of substances in or out of the cell from or to the
environment.
Cells larger than 1 mm in
diameter may not be viable because the rate of diffusion is too
slow to supply nutrients and oxygen sustain the cell's
life-supporting biochemistry.
Multicellular organisms, with
many layers of cells, tend to have a smaller surface to volume ratio
and therefore need specialised organ systems with large surface
areas for the efficient transfer of substances and also thermal
energy to avoid heating.
Because multicellular
organisms have many layers of cells, this increases the time
needed for nutrients and oxygen to diffuse in and reach the
inner cells.
Therefore the cells of the
outer layers would tend to use up the resources first and
faster, depriving inner cells life-supporting resources.
Therefore adaptations have
evolved to enable complex multicellular organisms to overcome
this problem.
