Biology · Transport in Cells
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Surface Area to Volume Ratio and Exchange Surfaces
A single cell can get what it needs by diffusion through its surface, but a whole animal cannot. This lesson shows how to calculate a surface area to volume ratio, why size matters, and how exchange surfaces in animals and plants are adapted.
Learning Objectives
- 1Calculate and compare surface area to volume ratios.
- 2Explain why a single-celled organism can exchange materials across its surface.
- 3Explain why multicellular organisms need exchange surfaces and a transport system.
- 4State what makes an exchange surface effective.
- 5Explain how the small intestine, lungs, gills, roots and leaves are adapted for exchanging materials.
Retrieval practice
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1
What three things affect the rate of diffusion?
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The concentration gradient, the temperature and the surface area of the membrane.
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2
What is diffusion?
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The net movement of particles from a higher to a lower concentration.
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3
Name one substance that diffuses out of respiring cells.
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Carbon dioxide.
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4
Which waste product diffuses from cells into the blood plasma?
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Urea.
Why size matters
Last lesson you saw that diffusion is faster with a larger surface area. This lesson turns that into numbers. The key idea is that when an object gets bigger, its volume grows faster than its surface area. A tiny organism has plenty of surface for its size and can live by diffusion alone. A large one does not, and it has evolved special organs to get round the problem.
Surface area and volume
Surface area is the total area of the outside of an object. Volume is the amount of space inside it.
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Surface area
For a cube, the area of one face is side × side, and there are six faces, so the surface area is \(6 \times \text{side}^{2}\).
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Volume
For a cube the volume is \(\text{side} \times \text{side} \times \text{side}\), which is \(\text{side}^{3}\).
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Surface area to volume ratio
Divide the surface area by the volume. It tells you how much surface there is for each unit of volume.
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Bigger means smaller ratio
As an object gets larger, the surface area to volume ratio falls.
Surface area to volume ratio of a cube
A cube has sides of 2 cm. Calculate its surface area to volume ratio.
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- 1 Find the area of one face \(2 \times 2 = 4\ \text{cm}^{2}\).
- 2 Multiply by 6 faces to get the surface area \(4 \times 6 = 24\ \text{cm}^{2}\).
- 3 Find the volume \(2 \times 2 \times 2 = 8\ \text{cm}^{3}\).
- 4 Divide the surface area by the volume \(24 \div 8 = 3\), so the ratio is 3 : 1.
Answer3 : 1
Bigger cubes have a smaller ratio
Make a cube three times as wide and its surface area to volume ratio falls from 6 : 1 to 2 : 1.
A block that is not a cube
A block measures 2 cm by 3 cm by 4 cm. Calculate its surface area to volume ratio, to one decimal place, in the form x : 1.
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- 1 Find the area of each pair of faces \(2 \times 3 = 6\), \(2 \times 4 = 8\) and \(3 \times 4 = 12\) cm². Each appears twice.
- 2 Add them up, doubling each \(2 \times (6 + 8 + 12) = 52\ \text{cm}^{2}\).
- 3 Find the volume \(2 \times 3 \times 4 = 24\ \text{cm}^{3}\).
- 4 Divide to get the ratio in the form x : 1 \(52 \div 24 = 2.17\), which is 2.2 : 1 to one decimal place.
Answer2.2 : 1
Small and large organisms
What this means for living things depends on how big they are.
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Single-celled organisms
A single cell has a relatively large surface area to volume ratio. Oxygen and food can diffuse in, and waste out, fast enough to meet the needs of the whole organism.
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Multicellular organisms
A large organism has a much smaller surface area to volume ratio. Substances would take far too long to diffuse from the outside to the cells in the middle.
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The answer
Large organisms have exchange surfaces, which are specialised surfaces for exchanging materials, and a transport system, such as the blood, to carry substances to and from every cell.
Why large organisms need exchange surfaces
In a large organism the cells in the middle are too far from the outside for diffusion alone.
What makes an exchange surface effective
In multicellular organisms, surfaces and organ systems are specialised for exchanging materials. The effectiveness of an exchange surface is increased by four things.
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A large surface area
More area means more particles can cross at once. Surfaces are often folded or divided into many small parts.
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A thin membrane
A thin layer gives a short diffusion path, so particles cross quickly.
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An efficient blood supply (animals)
Blood carries substances away, so the concentration on that side stays low and the gradient stays steep.
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Being ventilated (animals, for gas exchange)
Moving air or water keeps the concentration of the gas high on the outside of the surface.
Exchange surfaces in animals
Each of these organs has the features above. The names are worth learning.
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Small intestine
The inside wall is covered in villi, tiny finger-like folds that give a very large surface area. Each villus has a wall one cell thick and a network of capillaries, so digested food is absorbed quickly into the blood.
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Lungs
The air passages end in millions of tiny air sacs called alveoli, which give a large surface area. Each alveolus has a wall one cell thick and is wrapped in capillaries. Breathing ventilates the lungs.
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Gills (fish)
A gill is made of many thin filaments that give a large surface area. Each has a thin surface and a rich blood supply. Water flows over the gills all the time, which ventilates them.
Exchange surfaces in plants
Plants have exchange surfaces too. They are not ventilated or supplied with blood, but the other features are the same.
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Roots
Root hair cells have a long, thin extension that gives a large surface area for taking up water and mineral ions from the soil.
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Leaves
A leaf is flat, which gives a large surface area, and thin, which gives a short diffusion path. It has air spaces inside it and tiny pores called stomata on the underside, so carbon dioxide can diffuse in and oxygen can diffuse out.
Exchange surfaces in animals and plants
Five exchange surfaces, and the features they share.
Case study
The lining of the small intestine
If the inside of the small intestine were smooth, only a little of your food could be absorbed. It is a tube several metres long, and its lining is folded into millions of villi, so the area that touches the digested food is far larger than the area of a smooth tube would be. Each villus has a wall one cell thick, and the blood in its capillaries carries the absorbed food away, which keeps the concentration gradient steep.
Why exchange surfaces exist
The bigger the organism, the smaller its surface area compared with its volume.
So large organisms cannot rely on diffusion across their outer surface and need specialised exchange surfaces.
Surface area to volume ratio
Surface area to volume ratio
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Calculating
- surface area ÷ volume
- cube = 6 × side² ÷ side³
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Bigger object
- smaller ratio
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Single cell
- large ratio
- diffusion across the surface is enough
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Large organism
- small ratio
- needs exchange surfaces and a transport system
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Exchange surfaces
- large area
- thin
- blood supply
- ventilation
Summary and exam focus
- Surface area to volume ratio is surface area divided by volume. It gets smaller as an object gets bigger.
- A single-celled organism has a large ratio, so diffusion across its surface meets its needs.
- A multicellular organism has a small ratio, so it needs exchange surfaces and a transport system.
- Effective exchange surfaces have a large surface area and a thin membrane, and in animals a good blood supply and ventilation.
- The small intestine, lungs, gills, roots and leaves are all adapted this way.
Exam focus
Explain why a large multicellular organism needs an exchange surface and a transport system, but a single-celled organism does not. (4 marks) (4 marks)
Use the phrase "surface area to volume ratio" and compare the two organisms. Link small ratio to the slow diffusion of substances to the middle cells.
Key terms
The words this lesson expects you to use. Each one is linked from the first place it appears above.
- Surface area to volume ratio
- The surface area of an object divided by its volume.
- Exchange surface
- A specialised surface through which substances are exchanged between an organism and its surroundings.
- Transport system
- A system, such as the blood and blood vessels, that carries substances around a large organism.
- Diffusion path
- The distance particles have to travel to cross an exchange surface.
- Villi
- Tiny finger-like folds in the lining of the small intestine that increase its surface area.
- Alveoli
- The tiny air sacs at the ends of the airways in the lungs, where gas exchange takes place.
- Gill
- The organ a fish uses to take oxygen from water, made of many thin filaments.
- Root hair cell
- A cell in the root with a long thin extension that increases the surface area for taking up water and ions.
- Stomata
- Tiny pores in the surface of a leaf that let gases in and out.
- Ventilation
- Moving air or water over an exchange surface so that the concentration gradient stays steep.
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