Why Are Cells Small?

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Cell Size Math

First of all, the SURFACE AREA (abbreviation = SA) is the area of material that it would take to completely cover an object.

• For a simple cube shape, surface area is simply the length of one side times the height of one side times the number of sides (all cubes have, incidentally, 6 sides).

The formula can be written like this: 

Surface Area = Length x Height x 6

• For example, a cube that was 3 cm on each side would have a surface area of:
SA = 3 cm x 3 cm x 6 = 54 cm²
Notice that the units are "square" units.

• VOLUME (V) is the amount of space inside an object.

• Volume for a simple cube is equal to the length times the height times the depth of an object.

V = L x H x D

For the above example of a 3 cm cube, the volume would be:
V = 3 cm x 3 cm x 3 cm = 27 cm³
Notice that the units are "CUBIC" units.

The surface area to volume ratio (SA:V) is the proportion of area of material covering an object to amount of material within the object. i.e. it is a measure of how much covers the object for each unit of interior volume.
For the above example:

SA:V
54:27

(this ratio can be reduced to smaller numbers similar to the way that fractions can be reduced. It is customary to reduce SA:V ratios so that V is equal to 1. This can be done by dividing the SA by V and V by V as below)

54/27: 27/27
2:1

• The surface area to volume ratio for the above cube is equal to 2:1. That is, for every 2 units of surface area covering the outside of the cube, there is 1 unit of volume in the inside of the cube. If this cube were a cell, we could further say that there are 2 units of cell membrane for every unit volume of cytoplasm in its interior.

Extra Practice

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