Surface Area to Volume Ratio Explained
How to calculate surface area to volume ratio using cubes, why the ratio falls as size increases, and what that means for diffusion in cells. Includes the 4-mark exam question, a worked model answer and the examiner trap on saying larger organisms have a larger ratio.
Chapters (9)
Exam question [4 marks]
A cube-shaped organism has sides of 2 cm. Calculate its surface area to volume ratio. Explain why a much larger organism of the same shape cannot rely on diffusion across its surface alone.
Try it on paper first, then check the mark scheme below. The question is original and was written for this lesson.
Mark scheme
| Mark | Mark point | Also accept | Do not accept |
|---|---|---|---|
| 1 | Surface area = 24 cm squared and volume = 8 cm cubed (both required) | working shown: 6 x (2 x 2) = 24 and 2 x 2 x 2 = 8 | surface area of one face only (4); volume given as 6 |
| 2 | Surface area to volume ratio = 3 : 1 | "3", "3:1", 24 / 8 | "1 : 3" or 8 / 24 (wrong way round) |
| 3 | As size increases, volume increases faster than surface area, so the surface area to volume ratio decreases | "surface area to volume ratio gets smaller", "volume increases by a greater factor", "surface area increases by a smaller factor than volume" | "larger organisms have a larger surface area, so a larger ratio"; "surface area decreases" |
| 4 | Surface area is too small for the volume of cells / diffusion distance is long, so diffusion is too slow to supply the needs of all the cells | "not enough surface to supply all the cells", "long distance from surface to the centre", "cannot meet demand for oxygen and nutrients" | "it cannot diffuse" with no reference to surface area, volume or distance |
Marks 1 and 2 are the calculation (a correct ratio from a correct surface area and volume also earns mark 2 if mark 1 was lost through an arithmetic slip: error carried forward). Marks 3 and 4 explain the trend and its consequence. Always give surface area first in the ratio. Units: cm squared for area, cm cubed for volume. Do not credit "larger surface area" as the reason; the ratio is what falls.
Model answer (4/4)
Surface area = 6 x 2 x 2 = 24 cm squared. Volume = 2 x 2 x 2 = 8 cm cubed. The ratio is 24 : 8, which is 3 : 1. As an organism gets larger, its volume increases faster than its surface area, so the surface area to volume ratio decreases. In a large organism the surface area is too small for the volume of cells and the diffusion distance to the centre is long, so diffusion alone is too slow to supply all the cells.
Examiner trap
- Calculating the wrong ratio (should be SA:V)
- Saying larger organisms have a larger SA:V
- Mixing up surface area and volume units
Key terms
- surface area to volume ratio
- diffusion
- exchange surface
- volume
- surface area
Lesson notes
A written version of the video, chapter by chapter, for revision. Times link to the video.
0:29One cube: surface area and volume
Take a cube with sides of one centimetre. Surface area is the total area of the outside. A cube has six faces, and each face is one centimetre by one centimetre. So the surface area is six square centimetres. Volume is the space inside. One by one by one is one cubic centimetre.
Notice the units. Surface area is squared, volume is cubed.
0:57The ratio as a number
The surface area to volume ratio is the surface area divided by the volume. Surface area first, volume second. Get that order wrong and you lose the mark. Here, six divided by one gives six to one.
1:12A cube twice the size
Now double the side to two centimetres. This is the cube in our question. One face is two times two, so four square centimetres. Six faces, so twenty four square centimetres. Volume is two times two times two, so eight cubic centimetres. Twenty four divided by eight is three. The ratio is three to one.
1:36A cube four times the size
Double again, to four centimetres. Each face is four by four, which is sixteen. Six faces make ninety six. Volume is sixty four. Ninety six divided by sixty four is one point five. Look at the ratios. Six, three, one point five.
As the cube gets bigger, the ratio falls.
1:59Graphing the pattern
Why does it fall? Surface area goes up with length squared. Volume goes up with length cubed. So volume grows faster than surface area, and the ratio drops. The rule to remember: larger organisms have a smaller surface area to volume ratio.
2:17Why cells stay small
Now link it to living things. Every cell needs oxygen and nutrients, and has to get rid of waste. A single celled organism is tiny, so its ratio is large. Substances only travel a short distance to reach the middle, so diffusion across the surface is enough. In a large organism, the ratio is small. There is not enough surface for all the cells inside, and the distance from the surface to the centre is long, so diffusion alone is too slow. Metabolic rate matters too. Cells use oxygen in proportion to their volume, but supply comes through the surface, so a small ratio means less surface for each unit of metabolism.
Large organisms get round this with flatter or folded shapes that raise the ratio, and with special exchange surfaces and transport systems. We meet those in the next lesson.
3:52Examiner trap and recap
The trap. Do not say a larger organism has a larger ratio. It has a larger surface area, but a smaller ratio. Recap. Volume grows faster than surface area, so bigger means a smaller ratio, and diffusion alone stops being enough.
Next, how big bodies cope, with new shapes and special systems.
Keep going
More from 3.3 Exchange with the environment
- SA:V Ratio, Body Size and Metabolic Rate · AQA 7402 · 3.3.1
- Gas Exchange: Single Cells and Insects · AQA 7402 · 3.3.2
- Fish Gills and the Counter-current Principle · AQA 7402 · 3.3.2
- Gas Exchange in Leaves: Mesophyll and Stomata · AQA 7402 · 3.3.2
All 10 3.3 Exchange with the environment lessons Whole playlist on YouTube
Independent revision resource, not affiliated with or endorsed by AQA. The exam question is original and was written for this lesson; it is not an AQA question. Spotted an error? Email info@medservatory.com with the lesson code AB-051.