Surface area to volume ratio
AQA
A-Level
Surface area increases with the square of a linear dimension while volume increases with its cube, so as an organism or structure gets larger its surface area to volume ratio falls. A 1 mm cube has 6 mm² of surface and 1 mm³ of volume, a ratio of 6:1; a 2 mm cube has 24 mm² over 8 mm³, a ratio of 3:1. The biological consequence is that exchange happens across surfaces while demand is generated throughout the volume. A large organism therefore has proportionally less surface through which to absorb oxygen and nutrients and to lose heat and waste, and the distance from the surface to the innermost cells becomes too great for diffusion to supply them in time. Small organisms can rely on diffusion across the body surface alone.
9
Objectives
9
Exam Tips
13
Pitfalls
16
Key Terms
15
Mark Points
Subtopics in this area
The relationship between the size of an organism or structure and its surface area to volume ratio.
Changes to body shape and the development of systems in larger organisms as adaptations that facilitate exchange as this ratio reduces.
Students should be able to appreciate the relationship between surface area to volume ratio and metabolic rate.
Surface area to volume ratio Revision Guide
Learning Objectives
What you need to know and understand
- Calculate the surface area to volume ratio of a cube or a named structure and express it as a ratio to 1 to the required number of significant figures.
- Explain why the ratio falls as size increases, using the square and cube relationship.
- Predict, for two organisms of different size, which relies on diffusion across the body surface and justify the answer using the ratio.
- Explain why a flatworm can rely on diffusion while a mammal of the same mass cannot.
- Describe two body shape adaptations and two systems that compensate for a low surface area to volume ratio.
- Suggest how the body shape of a mammal living in a cold climate differs from one in a hot climate, and justify the difference in terms of the ratio.
- Explain why a small mammal has a higher metabolic rate per unit mass than a large one.
- Describe an inverse relationship between body mass and oxygen consumption per gram using figures from a graph.
- Predict how heart rate, breathing rate and food intake differ between a shrew and an elephant, and justify each prediction.
Marking Points
Key points examiners look for in your answers
- one mark for correct calculation of surface area and of volume in the same units
- one mark for dividing surface area by volume and expressing the answer as a ratio to 1
- one mark for each correct row where the question supplies a table to complete, using the values given in that question
- one mark for stating that as size increases volume increases faster than surface area, so the ratio falls
- one mark for linking the falling ratio to exchange: proportionally less surface for the same demand, and longer diffusion distances
- State that a larger organism has a smaller surface area to volume ratio, meaning diffusion across the body surface alone is too slow to meet metabolic needs.
- Describe a change in shape that keeps diffusion distances short, such as a flattened body, or folding that increases surface area.
- Explain the development of a specialised exchange surface, such as lungs, gills or a tracheal system, to compensate for a low SA:V ratio.
- Identify that a mass transport system is required to carry substances between the exchange surface and the cells.
- Explain that ventilation or blood flow maintains the concentration gradient across the exchange surface.
- State that the smaller organism has a larger surface area to volume ratio.
- Explain that heat is lost across the surface more rapidly relative to body mass.
- Link rapid heat loss to a higher rate of respiration, or metabolic rate per unit mass, to replace the heat lost and maintain body temperature.
- Connect the resulting higher oxygen demand to the requirement for faster ventilation, a faster heart rate, or a larger relative exchange surface.
- When describing a trend in data, quote specific figures from the graph before explaining the biological cause.
Examiner Tips
Expert advice for maximising your marks
- 💡Write surface area divided by volume as a line of working before using the calculator; a method mark is available even if the final value is wrong.
- 💡Read the significant figures instruction twice and round only at the end of the calculation.
- 💡Compare ratios, not raw surface areas, whenever the question involves two organisms of different size.
- 💡Every adaptation needs a consequence: flattened body, so short diffusion distance, so diffusion alone is fast enough.
- 💡In cold-climate or hot-climate questions, say which way the ratio changes before explaining the effect on heat loss.
- 💡Name the three systems, exchange surface, mass transport, ventilation, rather than writing generally about being 'more complex'.
- 💡Always attach 'per unit mass' or 'per gram' to metabolic rate when comparing organisms of different sizes.
- 💡Describe first, then explain: state the trend with two sets of figures, then give the ratio explanation.
- 💡Check what the question is asking for before writing about surface area to volume ratio; in some specific gas exchange adaptation questions, it may not be the focus.
Common Mistakes
Pitfalls to avoid in your exam answers
- giving the ratio the wrong way round, as volume to surface area
- mixing units, for example µm² with mm³, before dividing
- quoting an unrounded value when the question asks for a given number of significant figures
- saying a larger organism has a smaller surface area, when it has a larger area but a smaller ratio
- writing no working, so the method mark is lost when the arithmetic slips
- Saying large organisms need more oxygen so they have lungs, with no reference to the ratio or to diffusion distance. Correction: Always link the need for lungs to a decreasing SA:V ratio and increased diffusion distances.
- Describing a lung as increasing volume rather than surface area. Correction: Emphasise that folding in lungs increases surface area to maximise diffusion.
- Treating body shape adaptations as being only about heat, and ignoring exchange. Correction: Remember that SA:V ratio affects both heat loss and the exchange of respiratory gases.
- Writing that diffusion does not work in large organisms, rather than that it is too slow over long distances. Correction: State that diffusion is too slow to meet the metabolic demands of large organisms.
- Saying small animals have a higher metabolic rate without the qualification 'per unit mass'; a whale's total metabolic rate is far greater.
- Reversing the ratio and claiming large animals have the larger surface area to volume ratio.
- Explaining heat loss but failing to link it to respiration rate and oxygen demand.
- Describing a graph trend without using any figures from the axes.