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Exchange surfaces · cell size
Surface area to volume ratio
Calculate surface area, volume and surface area to volume ratios for cubes and spheres. Practise rearranging a ratio into x:1.
Method and worked examples ↓Learn the method
How to approach these questions
- Use the same length unit throughout the calculation.
- Calculate surface area in square units and volume in cubic units.
- Divide surface area by volume. To express SA:V as x:1, divide both terms by the volume.
- For similarly shaped objects, increasing size decreases surface area per unit volume. This helps explain the need for specialised exchange surfaces.
Worked examples
A cube has a side of 3 mm. Find its surface area, volume and SA:V.
Surface area = 6 × 3² = 54 mm². Volume = 3³ = 27 mm³. SA:V = 54:27 = 2:1, using these units. SA/V is 2 mm⁻¹.
A sphere has a radius of 6 μm. Find its SA/V using 3/r.
SA/V = 3 ÷ 6 = 0.5 μm⁻¹. Radius is half the diameter, so do not substitute a diameter of 12 μm into 3/r.
Keep practising
Topic map and study list · Practical data guides · Active recall decks
Course resources
AQA A-level Biology · OCR A A-level Biology · Textbook answers
Skill coverage follows the common A-level science subject content. Check your board’s current requirements: AQA 7402 and OCR A H420.