Surface area to volume ratioAQA A-Level Biology: Revision notes
Section 1
Size and surface area to volume ratio
The surface area to volume ratio (SA:V) compares the surface through which exchange happens with the volume of tissue that needs supplying. As an organism or structure gets larger, its volume increases faster than its surface area, so the ratio decreases.
Worked example (cubes): surface area = 6 × side²; volume = side³.
- Side 1 cm: SA 6 cm², volume 1 cm³, SA:V = 6 : 1
- Side 2 cm: SA 24 cm², volume 8 cm³, SA:V = 3 : 1
- Side 4 cm: SA 96 cm², volume 64 cm³, SA:V = 1.5 : 1
For a cuboid, surface area is the sum of the areas of all six faces. Give the ratio in the form x : 1, or divide area by volume.
Do not say a larger organism has a smaller surface area. Its surface area is bigger, but the ratio of surface area to volume is smaller.
Section 2
Why the ratio matters for exchange
Oxygen and nutrients are used by every cell, so demand depends on volume, while exchange with the environment takes place across the surface.
- Small organisms (such as single-celled organisms) have a large SA:V and a short diffusion distance, so diffusion across the body surface is sufficient
- Larger organisms have a smaller SA:V and long diffusion distances, so diffusion across the body surface alone is too slow to supply the cells in the centre
Section 3
Adaptations as the ratio falls
Larger organisms overcome the problem in two ways.
Changes to body shape that increase the ratio:
- Flattened bodies (for example flatworms) or thin, branching structures keep distances short
- Large thin ears or extensions increase the surface area for heat loss
Development of specialised systems (necessary as the ratio gets smaller):
- Exchange organs with a large surface area, for example lungs and gills
- Mass transport systems, such as a circulatory system, to carry substances to cells
- Digestive systems to absorb nutrients
Section 4
Metabolic rate and heat loss
Heat is produced by the respiring cells in the volume of the body and lost across the surface. Small mammals have a large SA:V, lose heat quickly and must have a high metabolic rate per gram of body mass to maintain body temperature, so they need to eat large amounts of food.
Large mammals have a small SA:V and lose heat slowly; their problem is overheating, so they may have large thin ears or use behaviours that increase heat loss.
Animals in cold climates tend to be compact and rounded with small extremities (small SA:V); animals in hot climates tend to have large extremities (large SA:V).
In explanations, state that heat is produced by volume and lost across surface area, then link to ratio and metabolic rate per gram.
Section 5
Calculating the ratio
For exam questions, calculate the surface area of each face, add them up, then divide by the volume.
Worked example: a cuboid 2 cm × 3 cm × 4 cm. Faces: 2 × (2 × 3) + 2 × (2 × 4) + 2 × (3 × 4) = 12 + 16 + 24 = 52 cm². Volume = 2 × 3 × 4 = 24 cm³. SA:V = 52 ÷ 24 = 2.17 : 1 (3 s.f.).
Show your working and include units (cm², cm³). The ratio itself has units of cm⁻¹ but is normally given as x : 1.
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Surface area to volume ratio
- Biology students make cube-shaped models of organisms to investigate how size affects the exchange of substances. They compare a small cube with sides of 3 cm and a larger cube with sides of 6 cm.Explain why an organism the size of the 6 cm cube is less able to exchange substances by diffusion across its body surface alone than one the size of the 3 cm cube.2 marks
- A shrew has a body mass of about 8 g and must feed almost continuously. An elephant has a body mass of about 4000 kg and eats for much of the day, but eats far less food for each kilogram of its body mass. Both are mammals that maintain a constant body temperature.Elephants have very large, thin ears with many blood vessels near the surface. Explain how this helps an elephant to lose heat despite its small surface area to volume ratio.2 marks
- Two cube-shaped model organisms are made. Organism A has sides of 1 cm and organism B has sides of 4 cm. The cells in both models respire at the same rate for each cm³ of volume.Calculate the surface area to volume ratio of organism A and of organism B. Show your working.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).