Surface area to volume ratioEdexcel A-Level Biology B: Revision notes
Section 1
Surface area to volume ratio
The surface area to volume ratio (SA:V) compares the surface through which substances enter or leave an organism with the volume of cells that need supplying. For a cube of side s: SA = 6s², V = s³, so SA:V = 6/s. For a sphere: SA = 4πr², V = 4/3 πr³, so SA:V = 3/r.
Worked example: a cube of side 4 mm has SA = 96 mm² and V = 64 mm³, so SA:V = 1.5 mm⁻¹ (or 1.5 : 1). A cube of side 2 mm has SA:V = 3 mm⁻¹.
As an object gets larger, volume increases faster than surface area, so SA:V decreases.
Compare ratios, not just surface areas. A bigger cube has a larger surface area but a smaller SA:V.
Section 2
Effect on the transport of molecules
Oxygen, nutrients and waste move into and out of cells by diffusion. The rate of diffusion increases with a larger surface area and a steeper concentration gradient, and decreases with a longer diffusion distance.
In small organisms such as bacteria or flatworms, SA:V is large and no cell is far from the surface, so diffusion across the body surface meets the needs of all the cells.
In larger organisms, the demand for oxygen depends on volume while supply depends on surface area, so a smaller SA:V means the surface cannot supply enough. The distance to central cells is also too long for diffusion alone.
Section 3
Why large organisms need a mass transport system
Mass transport systems (such as the circulatory system) move substances in bulk, by pressure differences, between the exchange surfaces and the cells. They are needed because:
- SA:V of a large organism is small, so the body surface cannot supply all cells
- diffusion distances to inner cells are too long
- large and active organisms have high metabolic demands.
Flat organisms (e.g. flatworms) and organisms with very low metabolic rates can avoid a mass transport system because every cell is close to the surface.
Section 4
Specialised gas exchange surfaces
Large organisms have specialised exchange surfaces, such as lungs, gills and the leaf's air spaces. They increase the effective surface area for exchange and share features:
- a large surface area, often through folding or many small units
- thin surfaces, giving a short diffusion distance
- a steep concentration gradient, maintained by ventilation and a good blood supply that carries substances away
These surfaces compensate for the small SA:V of the whole body, and are linked to a mass transport system.
In exam answers, link each feature to its effect: a thin surface gives a short diffusion distance, a large area gives more diffusion, and a blood supply keeps the gradient steep.
That's the notes covered.
Carry on to the next subtopic.
Exam questions on Surface area to volume ratio
- A student made cubes of agar jelly containing a pH indicator, with sides of 2 mm, 4 mm and 8 mm, to model cells of different sizes. She placed them in dilute acid and timed how long the acid took to change the colour of the whole cube. (Surface area of a cube = 6 x side squared; volume = side cubed.)The 8 mm cube took much longer to change colour completely than the 2 mm cube. Explain this result.2 marks
- The planarian is a flatworm about 15 mm long, 3 mm wide and less than 0.5 mm thick. It has no lungs, gills or blood. Its cells use oxygen from the water around it, which diffuses in across its body surface. A human, by contrast, is about 1.7 m tall and has lungs and a circulatory system.Explain how the shape of the planarian allows it to obtain enough oxygen without a circulatory system.2 marks
- A spherical bacterium has a diameter of 2 µm, and a spherical human cell has a diameter of 20 µm. A human adult is a large multicellular organism made of many cells of this size. (Surface area of a sphere = 4πr²; volume of a sphere = 4/3 πr³.)Calculate the surface area to volume ratio of each cell and state how many times greater it is for the bacterium than for the human cell.3 marks
Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).