Surface Area to Volume Ratio: AQA A Level Biology Exam Questions by Topic

AQASurface Area to Volume RatioExam Questions
Written by Tom Whitburn

Surface area to volume ratio (AQA 3.3.1) is the short section that opens 'Organisms exchange substances with their environment', and the idea runs through everything after it: gas exchange, digestion, mass transport and even why a mouse eats so much for its size. You need to know that as an organism or structure gets bigger its surface area to volume ratio gets smaller, how larger organisms make up for this with flattened or long, thin shapes and specialised exchange and transport systems, how the ratio links to metabolic rate through heat loss, and how to calculate a ratio from dimensions or a formula.

The examiners' reports show where the marks go. Students give one example instead of describing the relationship, name a body feature without saying how it helps diffusion, say respiration 'produces energy', divide volume by surface area, round 23.75 to 24 and call it three significant figures, and forget to count every face when a cube is cut into smaller cubes.

Start with the questions on size and diffusion, then larger organisms, then metabolic rate, and finish with the calculations. Answer each on paper before you open the mark scheme. If you'd like help with this topic, my AQA masterclasses run online on Tuesdays at 5.15pm for Year 12 and on Wednesdays or Thursdays at 6.30pm for Year 13.

What you need from GCSE and Year 12

Each question on this page assumes you're secure on these GCSE and Year 12 ideas. If any of them feels shaky, revise it before you start.

  • GCSE: surface area of a cube or cuboid is the total area of all six faces, and volume = length × width × height.
  • GCSE: single-celled organisms exchange substances by diffusion across their surface; larger organisms need exchange surfaces and transport systems.
  • GCSE: the rate of diffusion is faster with a larger surface area, a steeper concentration gradient and a shorter diffusion distance.
  • GCSE: mammals keep a constant body temperature, and respiration releases energy, some of it as heat.
  • Year 12 (AQA 3.1.6): ATP is made in respiration and releases energy for the cell when it is hydrolysed. See the ATP page.

Key terms

These words come up in the questions and mark schemes. Examiners expect you to use them exactly.

  • Surface area to volume ratio: surface area divided by volume, written as x : 1. It gets smaller as an organism or structure gets bigger.
  • Surface area: the total area of an object's outer surface; for a cube of side l it is 6l².
  • Volume: the space an object takes up; for a cube of side l it is l³.
  • Diffusion pathway: the distance a substance has to diffuse; a short (thin) pathway gives faster diffusion.
  • Exchange surface: a specialised surface, such as gills, alveoli or villi, that is large and thin so substances are exchanged quickly.
  • Mass transport system: a system, such as the blood circulation, that carries substances in bulk between exchange surfaces and the rest of the body.
  • Metabolic rate: the rate of the chemical reactions in an organism, often measured as the rate of oxygen uptake because oxygen is used in respiration.
  • Heat loss: heat lost across the body surface; an animal with a larger surface area to volume ratio loses heat faster.
  • Significant figures: the digits that carry meaning, counted from the first non-zero digit; 23.8 has three, 24 has two.

What these questions cover (AQA 3.3.1)

The questions test these statements from the AQA AS and A-level Biology specification (7401/7402):

  • Size and ratio: The relationship between the size of an organism or structure and its surface area to volume ratio.
  • Larger organisms: 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.

How to use this page

Write your answer on paper before you open the mark scheme. Allow about 1.3 minutes per mark: the 14 questions are worth 30 marks, so about 39 minutes in total. Then mark your answer strictly against the mark scheme and read the examiners' tip underneath it. If you'd rather print the questions, download the PDF pack.

Size and surface area to volume ratio (3.3.1)

Question 1

AS Paper 2 · June 2018 · Q03.1 · 1 mark · Easy

Describe the relationship between the size of an organism and its surface area to volume ratio.

Question text: describe the relationship between size and surface area to volume ratio of organisms, 1 mark.
Show the mark scheme Mark scheme: as size increases, the surface area to volume ratio decreases. Accept the converse; a comparison is needed, for example smaller organisms have a larger ratio.

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From the examiners' report: 70.3% got this. Describe the trend across all sizes ('as size increases, the ratio decreases'), not one example such as 'large organisms have small ratios', and don't drift into diffusion or gas exchange.

Question 2

AS Paper 2 · June 2016 · Q03.2 · 2 marks · Medium

Explain how two features of a tubifex worm's body allow efficient gas exchange.

Information from earlier in this question:

Earlier part of the same exam question, giving the information this part uses. Introduction: tubifex worms are small, thin animals that live in water with no specialised gas exchange or circulatory system; Figure 2 shows a long, thin segmented worm. Question: explain how two features of its body allow efficient gas exchange, 2 marks.
Show the mark scheme Mark scheme: thin or small, so short diffusion pathway; flat, long, small or thin, so large surface area to volume ratio. Reject thin membrane, wall or cells.

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From the examiners' report: Almost two thirds scored at least one mark. Name a body feature and then say what it does: thin body so a short diffusion pathway, long and thin so a large surface area to volume ratio. A 'thin membrane' doesn't count.

Question 3

A level Paper 1 · June 2019 · Q07.1 · 1 mark

Suggest how the alga Ulva lactuca survives without xylem tissue.

Figure 6: diagram of the alga Ulva lactuca, a thin, flat, leaf-like thallus attached to rock by a holdfast. Question: suggest how Ulva survives without xylem tissue, 1 mark.
Show the mark scheme Mark scheme: short diffusion pathway to cells, or its whole surface is permeable to water and ions. Accept not needing support because the water supports it. Ignore pores or stomata.

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From the examiners' report: There's no examiners' report for this paper, so this tip comes from the mark scheme. A thin, flat alga has a short diffusion pathway, so water and ions reach every cell by diffusion across its surface.

Question 4

AS Paper 1 · November 2021 · Q03.4 · 2 marks

Use surface area to volume ratio to explain why mitochondria sit near the membrane in large cells.

Information from earlier in this question:

Earlier part of the same exam question, giving the information this part uses. Introduction: Figure 3, photograph of the single-celled eukaryote Uronema marinum taken through an optical microscope, with length Y–Z marked. Question: in large cells most mitochondria are close to the cell-surface membrane; use surface area to volume ratio to suggest why, 2 marks.
Show the mark scheme Mark scheme: larger cells have a smaller surface area to volume ratio; so it takes longer for oxygen to diffuse to the mitochondria, or the diffusion pathway is longer. Accept the converse.

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From the examiners' report: There's no examiners' report for this paper, so this tip comes from the mark scheme. Link the two ideas: a larger cell has a smaller ratio, so oxygen has further to diffuse to mitochondria in the middle.

Body shape and exchange systems in larger organisms (3.3.1)

Question 5

A level Paper 1 · November 2021 · Q02.1 · 2 marks

Explain the advantage for larger animals of a specialised system for oxygen uptake.

Question text: explain the advantage for larger animals of having a specialised system that facilitates oxygen uptake, 2 marks.
Show the mark scheme Mark scheme: larger organisms have a smaller surface area to volume ratio (or the converse); the system overcomes the long diffusion pathway, or gives faster diffusion.

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From the examiners' report: Most answers stated the size and ratio relationship, but few gave the reason for the second mark. Finish the argument: the specialised system overcomes the long diffusion pathway.

Question 6

AS Paper 1 · June 2019 · Q06.4 · 2 marks

Conclude how the gills of three deep-sea fish species are adapted to oxygen concentration.

Information from earlier in this question:

Earlier part of the same exam question, giving the information this part uses. Introduction: Figure 5, line graph of relative oxygen concentration against water depth from 0 to 1400 m, falling to a minimum near 800 m then rising; Table 4, depth range and ratio of gill surface area to body mass for three fish species: Anoplopoma fimbria 148 : 1, Careproctus melanurus 124 : 1, Embassichtys bathybius 20 : 1. Question: what can you conclude about the adaptation of their gas exchange surfaces, 2 marks.
Show the mark scheme Mark scheme: generally, the lower the oxygen concentration, the higher the ratio of gill surface area to body mass; this supplies enough oxygen for respiration.

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From the examiners' report: There's no examiners' report for this paper, so this tip comes from the mark scheme. Link the two data sets: species living where oxygen is scarcest have the largest gill surface area per gram, which gets enough oxygen for respiration.

Surface area to volume ratio and metabolic rate (3.3.1)

Question 7

A level Paper 3 · June 2024 · Q03.1 · 3 marks · Medium

Describe and explain the relationship between surface area to volume ratio and metabolic rate in humans.

Question text: describe and explain the relationship between surface area to volume ratio of the human body and metabolic rate, 3 marks.
Show the mark scheme Mark scheme: as surface area to volume ratio increases, metabolic rate increases; a larger ratio loses more heat; a higher rate of respiration releases or replaces heat, maintaining body temperature. Accept the converse. Reject produces energy or heat energy.

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From the examiners' report: Only about 15% scored all three and over a third scored nothing. Answer about the human body, not mice and elephants, state the relationship, then link it to heat loss and respiration releasing heat. Energy is never 'produced'.

Question 8

AS Paper 2 · June 2018 · Q03.5 · 1 mark

Explain why oxygen uptake is a measure of metabolic rate.

Question text: explain why oxygen uptake is a measure of metabolic rate in organisms, 1 mark.
Show the mark scheme Mark scheme: oxygen is used in respiration, which provides energy or ATP; or oxygen is used in respiration, which is a metabolic process. Reject produces energy and references to anaerobic respiration.

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From the examiners' report: Only 25.1% got this. Name respiration and then say why it matters: it provides the ATP for metabolism. Don't confuse respiration with breathing, or say energy is 'produced'.

Question 9

A level Paper 1 · June 2019 · Q09.4 · 3 marks

Use surface area to volume ratio to explain why a mouse has a higher metabolic rate than a horse.

Information from earlier in this question:

Earlier part of the same exam question, giving the information this part uses. Introduction: Table 7, partial pressures of oxygen at which horse and mouse haemoglobin are 50% and 25% saturated, and body mass of one animal (horse 550 000 g, mouse 23 g). Question: use surface area to volume ratio to explain the higher metabolic rate of a mouse, 3 marks.
Show the mark scheme Mark scheme: the mouse is smaller so has a larger surface area to volume ratio; more or faster heat loss per gram; a faster rate of respiration releases or replaces heat. Accept converse answers about the horse. Reject produce or generate heat.

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From the examiners' report: There's no examiners' report for this paper, so this tip comes from the mark scheme. Keep every point comparative (larger ratio, more heat lost) and say respiration releases or replaces heat, not 'produces' it.

Question 10

AS Paper 2 · June 2018 · Q03.6 · 3 marks · Hard

Explain why Table 2 doesn't allow a conclusion about stage of development and metabolic rate.

Information from earlier in this question:

Earlier part of the same exam question, giving the information this part uses. Introduction: Table 2, ratio of surface area to mass and mean rate of oxygen uptake for frog eggs (2904 : 1, no information), tadpoles (336 : 1, 5.7 µmol g⁻¹ h⁻¹) and adults (166 : 1, 1.3 µmol g⁻¹ h⁻¹). Question: explain why a student could not make a conclusion about stage of development and metabolic rate, 3 marks.
Show the mark scheme Mark scheme: no information about the egg; so cannot compare all three stages; no statistical test or comparison of standard deviations, or no measure of significant difference. Reject chi-squared or correlation coefficient.

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From the examiners' report: Most spotted the missing egg data, but a dash means no information, not a dead egg, and 'mean' means many tadpoles and frogs were measured. Explain why two stages aren't enough and mention the lack of a statistical test.

Calculating surface area to volume ratios (3.3.1)

Question 11

AS Paper 1 · June 2023 · Q05.1 · 2 marks · Hard

Calculate the surface area and surface area to volume ratio of two agar blocks.

Introduction: agar blocks coloured with an indicator, pink above pH 8; Figure 6, block C a 4 cm cube and block D a 2 cm by 2 cm by 16 cm cuboid. Table 2: both have a volume of 64 cm³; complete the surface area and the ratio as x : 1, 2 marks.
Show the mark scheme Mark scheme: C, surface area 96 cm², ratio 1.5 : 1; D, surface area 136 cm², ratio 2.125 : 1 (2.1 : 1 or 2.13 : 1 allowed). Marked as columns, error carried forward for the ratio.

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From the examiners' report: Many could find the surface areas, though the cuboid D caused more errors. Divide surface area by volume, not the other way round, and give the ratio as x : 1.

Question 12

A level Paper 1 · June 2022 · Q08.2 · 2 marks · Medium

Complete a table of surface area to volume ratios for healthy and damaged gill filaments.

Table 4: healthy fish gill, surface area 7.4 × 10³ µm², volume 2.3 × 10⁴ µm³, ratio blank; damaged gill, surface area 1.1 × 10⁴ µm², volume blank, ratio 0.13 : 1. Give answers to 2 significant figures, 2 marks.
Show the mark scheme Mark scheme: healthy ratio 0.32 : 1; damaged volume 8.5 × 10⁴ or 85 000 µm³. If no marks, 1 mark for 0.3217 or a number that rounds to 85 000, such as 84 615.

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From the examiners' report: Three-quarters scored at least 1 mark. The common errors were dividing volume by surface area and rounding wrongly: 84 615 to 2 significant figures is 85 000, not 84 000.

Question 13

A level Paper 3 · June 2024 · Q03.2 · 3 marks · Easy

Use formulae to find which of two adults has the smaller surface area to volume ratio.

Table 2: person A, height 181 cm, mass 90.90 kg; person B, height 149 cm, mass 62.62 kg. Surface area in m² = square root of (height in cm × mass in kg ÷ 3600); volume in m³ = mass in kg ÷ 1010. Question: deduce which person has the smaller ratio, to 3 significant figures, 3 marks.
Show the mark scheme Mark scheme: person A with a ratio of 23.7 : 1 or 23.8 : 1 for 3 marks. Partial credit for the right person not to 3 significant figures or not as a ratio, for the right ratio with person B, or for 2.14 and 1.61 or 0.09 and 0.062 in the working.

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From the examiners' report: Well answered: a third got all three. Many thought 24 : 1 was three significant figures; it's two, so write 23.8 : 1. Show the surface areas (2.14 and 1.61 m²) and volumes (0.09 and 0.062 m³).

Question 14

A level Paper 1 · June 2018 · Q02.2 · 3 marks · Hard

Calculate whether the rate of osmosis per mm² per minute differs between one large and eight small potato cubes.

Information from earlier in this question:

Earlier part of the same exam question, giving the information this part uses. Introduction: one 35 mm potato cube and an identical cube cut into eight equal smaller cubes were put in sucrose solution; Figure 3, total mass in g against time from 0 to 160 minutes, falling faster for the eight small cubes (B) than for the large cube (A). Question: is the rate of osmosis per mm² per minute different between A and B from 0 to 40 minutes? Use calculations, 3 marks.
Show the mark scheme Mark scheme: rate per mm² for both: 1.6 to 1.8 × 10⁻⁵ and 1.5 to 1.6 × 10⁻⁵ (3 marks for both, 2 for one). Otherwise 1 mark for surface areas of 7350 and 14 700 mm², 1 mark for rates of about 0.12–0.13 and 0.22–0.23 g per minute, and 1 mark for a rate divided by a surface area.

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From the examiners' report: Only 5% got both rates and 56.4% scored nothing. Find each rate from the graph, work out the total surface area of all the cubes (6 × 35² = 7350 mm²; 8 × 6 × 17.5² = 14 700 mm²), then divide, showing every step.

Where students lose marks (from AQA examiners' reports and mark schemes)

Each point below is followed by wording that gained marks.

  • Describe the trend, not one organism: 70.3% got the relationship, but others wrote about diffusion or gave a single example such as 'large organisms have small ratios' instead of a comparison.

    ✔ Gains credit: "As size increases, the ratio (of surface area to volume) decreases."

  • Link each body feature to diffusion: Almost two thirds scored on the tubifex worm, but many named body features without explaining how they help gas exchange, or quoted a large ratio without linking it to a feature. A 'thin membrane' was rejected.

    ✔ Gains credit: "Thin, so short diffusion pathway; flat/long, so large surface area to volume ratio."

  • Name respiration to link oxygen and metabolism: Only 25.1% explained why oxygen uptake measures metabolic rate. Many avoided the word respiration, confused it with breathing, or said energy was 'produced'.

    ✔ Gains credit: "(Oxygen used in) respiration, which provides energy/ATP."

  • More heat lost, so faster respiration to replace it: Only about 15% scored all three marks on the human body question and over a third scored nothing. Many wrote about mice and elephants instead of humans, or about diffusion distances, and 'produces energy' was rejected.

    ✔ Gains credit: "A larger surface area to volume ratio loses more heat; a higher rate of respiration releases/replaces heat to maintain body temperature."

  • Surface area divided by volume: In both the agar block and gill filament questions a common error was dividing volume by surface area.

    ✔ Gains credit: "C: 96 cm², 1.5 : 1; D: 136 cm², 2.125 : 1" and "0.32 : 1" for the healthy gill.

  • 24 : 1 is only two significant figures: A third got all three marks for comparing two adults, but many gave 24 : 1 when the question asked for three significant figures. Rounding 84 615 to 84 000 lost marks in the gill question too.

    ✔ Gains credit: "Person A, 23.8 : 1 (or 23.7 : 1)" and "8.5 × 10⁴ µm³".

  • Count every face of every cube: Only 5% found both rates of osmosis per mm² and 56.4% scored nothing. Few could find the surface area of the eight small cubes, and answers with no working couldn't earn method marks.

    ✔ Gains credit: "7350 mm² and 14 700 mm²"; rates of about 1.7 × 10⁻⁵ (A) and 1.5 × 10⁻⁵ (B) g per mm² per minute.

  • A dash means no data, not a dead egg: Most noticed there was no oxygen uptake data for the egg, but some said the dash meant the eggs were dead or didn't respire, and some thought 'mean' meant only one tadpole was measured.

    ✔ Gains credit: "No information about egg, so cannot compare all three stages; no statistical test."

Download the questions

Download the PDF pack (14 questions, mark schemes at the end)

Keep practising

Questions, mark schemes and examiners' report extracts © AQA.

Tom Whitburn
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