Surface Area to Volume Ratio (AQA A Level Biology): Revision Note
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What is surface area to volume ratio?
Surface area and volume are factors that affect the exchange of materials in organisms
Surface area: the total area of an organism that is exposed to the external environment
Volume: the total internal volume of an organism
As the overall size of an organism increases, the surface area : volume ratio decreases
This is because volume increases more rapidly than surface area as size increases
Maths skill: calculating SA:V ratio
The surface area : volume ratio can be calculated for objects of different shape
Different shapes may be used to represent the dimensions of different organisms, e.g. a bacterial cell may be represented by a cylinder
Worked Example
A researcher calculated that the diameter of a spherical toad egg was 1.794 mm.
Use the formulae provided to calculate the surface area : volume ratio of the toad egg.
Surface area of a sphere = 4πr2
Volume of a sphere = 
πr
Answer:
Step 1: determine r
The radius is half the diameter
1.794 ÷ 2 = 0.897
Step 2: determine the surface area of the toad eg
surface area = 4 x π x 0.8972
= 10.111 mm2
Step 3: determine the volume of the toad egg
volume = x π x 0.897
= 3.757 mm3
Step 4: determine the SA:V ratio
SA:V ratio is normally notated as x:1, so we need to convert 10.1:3.8 to this notation
First we convert the volume value to 1:
3.8 ÷ 3.8 = 1
Then we divide the SA value by the same factor:
10.1 ÷ 3.8 = 2.7
So our final ratio is:
2.7:1
Examiner Tips and Tricks
Make sure that you know how to calculate surface area and volume for the following shapes:
cube
cuboid
cylinder
sphere
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