Question 1Warm-upFoundation
A cube has sides of 1 cm. Calculate its surface area to volume ratio.
SA = 6 cm², V = 1 cm³.
Worked solution
- ;
- , so
Answer:
GCSE & IGCSE biology practice
Surface area to volume ratio questions and answers
The surface area to volume ratio (SA : V) compares how much surface an object has for its size. Small objects have a large SA : V, so substances can diffuse in and out quickly enough. Large organisms have a small SA : V, so they need exchange surfaces (like lungs and villi) and transport systems. Give the ratio as a single number (SA ÷ V), e.g. 6 for 6 : 1.
8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated .
Where surface area to volume ratio comes up
| GCSE (AQA) | Biology and Combined Science, Foundation and Higher: calculate and compare surface area to volume ratios, and explain why multicellular organisms need exchange surfaces and transport systems. |
|---|---|
| Cambridge IGCSE (0610) | Listed in the syllabus's mathematical requirements: understand surface area and use the surface area : volume ratio. |
The method
- Surface area of a cube = 6 × side². Volume = side³.
- Cuboid: surface area = 2 × (lw + lh + wh); volume = l × w × h.
- SA : V = surface area ÷ volume.
- As size increases, SA : V decreases.
Surface area to volume ratio questions
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Warm-up
Question 2Warm-upFoundation
A cube has sides of 2 cm. Calculate its SA : V ratio.
SA = 24, V = 8.
Worked solution
- ;
Answer:
Exam-style
Question 3Exam-styleFoundation
A cube has sides of 3 cm. Calculate its SA : V ratio.
SA = 54, V = 27.
Worked solution
- ;
Answer:
Question 4Exam-styleFoundation
A cuboid measures 1 cm × 1 cm × 4 cm. Calculate its SA : V ratio.
SA = 2 × (1 + 4 + 4).
Worked solution
- ;
Answer:
Question 5Exam-styleFoundation
Which has the larger surface area to volume ratio?
SA : V falls as size increases.
Worked solution
- Smaller organisms have more surface for their volume.
Answer: A mouse: smaller organisms have a larger SA : V
Question 6Exam-styleFoundation
A cuboid measures 2 cm × 2 cm × 6 cm. Calculate its SA : V ratio to 2 decimal places.
SA = 2 × (4 + 12 + 12).
Worked solution
- ;
Answer:
Challenge
Question 7ChallengeFoundation
A cube-shaped cell has sides of 10 µm. Calculate its SA : V ratio (in µm⁻¹).
SA = 600 µm², V = 1000 µm³.
Worked solution
- ;
Answer:
Question 8ChallengeFoundation
Why does a large multicellular organism need specialised exchange surfaces and a transport system?
Think about distances and surface per unit volume.
Worked solution
- Large organisms have a small SA : V and long diffusion distances, so they need exchange surfaces (lungs, villi, gills) and a circulatory system.
Answer: Its small SA : V means diffusion through the body surface alone is too slow
Common mistakes
- Forgetting a cube has 6 faces.
- Dividing volume by surface area.
- Thinking larger objects have the bigger ratio.
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Sources
The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 27 October 2026:
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