# 3.1.1 Surface Area to Volume Ratio

### Surface Area to Volume Ratio

• Surface area and volume are both very important factors in the exchange of materials in organisms
• The surface area refers to the total area of the organism that is exposed to the external environment
• The volume refers to the total internal volume of the organism (total amount of space inside the organism)
• As the surface area and volume of an organism increase (and therefore the overall ‘size’ of the organism increases), the surface area : volume ratio decreases
• This is because volume increases much more rapidly than surface area as size increases

### Maths Skill: Calculating SA:V Ratio

• The surface area : volume ratio calculation differs for different shapes (these shapes can reflect different cells or organisms)

#### Worked Example

A researcher calculated the surface area of a large number of toad eggs. She calculated the mean surface area to be 10.12 mm2. Toad eggs are generally spherical. She calculated the surface area using the following equation: 4πr2

Use this equation to calculate the mean diameter of a toad egg. Give your answer to 3.s.f.

Step 1: Rearrange the equation to find the radius

r2 = surface area/4π

Step 2: Sub in relevant figures

r2 = 10.12 ÷ 12.56 = 0.805

Step 3: Find the square root of r2

Square root of 0.805 = 0.897

Step 4: Find the diameter from the radius

D = 2r

2(0.897) = 1.794

Step 5: Round to three significant figures

1.79 mm

#### Exam Tip

You are expected to be able to calculate the SA:V ratio for different shapes and explain how the increasing size of an organism affects the SA:V ratio. ### Author: Lára

Lára graduated from Oxford University in Biological Sciences and has now been a science tutor working in the UK for several years. Lára has a particular interest in the area of infectious disease and epidemiology, and enjoys creating original educational materials that develop confidence and facilitate learning.
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