Investigate surface-area-to-volume effects with agar
Agar blocks of different dimensions can compare diffusion penetration while controlling the solution, time and method.
AS Level · Cambridge International Biology 9700, 2028–2030. These lessons explain membrane transport and investigation reasoning. Written practice is self-checked; it does not demonstrate supervised practical competence or replace teacher-reviewed assessment.
Before you begin
- Relate phospholipid and protein structure to their roles, and distinguish a concentration gradient from the direction of net movement.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should remain the same when comparing agar blocks of different sizes?
What you will learn
- Plan an agar-block investigation of surface-area-to-volume ratio and diffusion
- Interpret the extent or proportion of diffusion without treating agar as a living cell
Compare blocks fairly
Prepare similar agar blocks with an indicator or substrate throughout. Place different sizes in the same diffusing solution for equal times and at the same temperature. Use consistent stirring, solution volume and start time.
After exposure, cut blocks using the same method and measure the penetration depth or the fraction of each block reached by the diffusing substance. Repeat measurements and calculate a mean if practical.
Link the observation to geometry
Smaller similar blocks have greater surface area relative to volume, so a larger fraction of their interior may be reached over the same time under comparable conditions. Distinguish the absolute penetration distance from the proportion of the block reached.
Agar is a non-living diffusion model. It has no cell membrane, active transport or metabolism. Interpret the result as evidence about diffusion distances and geometry, not a complete model of living tissues.
Pause and explain
Why can the small block show a greater fraction of its volume reached by diffusion?
Worked example
After equal exposure, a small agar cube changes colour throughout while a large cube has an unchanged centre. Explain the pattern.
Show the worked solution
- Diffusing particles enter from the surface.
- The small cube has a shorter maximum distance to its centre and higher SA:V.
Answer The diffusing substance enters from the block surface. The smaller cube has a higher surface-area-to-volume ratio and a shorter distance to its centre, so a greater fraction of its volume is reached within the same time.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Outline a fair agar-block investigation of diffusion and size.
Give me a hint
Change block size and control other diffusion conditions.
Compare my reasoning
- Use similar agar indicator blocks with different dimensions.
- Expose them for equal times in the same solution and measure penetration consistently.
Prepare similar agar blocks containing an indicator. Expose different-sized blocks to the same diffusing solution for equal times at controlled temperature and mixing. Cut each consistently and measure penetration depth or fraction changed; repeat trials.
Look for these in your work
- Size is the changed factor
- Exposure conditions and measurement controlled
A 1 cm cube is changed throughout after exposure, but only a 2 mm outer layer of a 3 cm cube changes. Explain why comparing changed fraction is useful.
Give me a hint
Calculate or reason about total versus proportional penetration.
Compare my reasoning
- Both received the same penetration depth near the surface.
- The smaller cube has a much larger fraction close to the surface.
The penetration depth is similar, but it reaches a much larger fraction of the 1 cm cube’s volume. Comparing changed fraction accounts for the different block sizes better than comparing surface layer thickness alone.
Look for these in your work
- Absolute depth distinguished from fraction
- Size effect explained
Give one conclusion and one limitation from an agar-block diffusion model.
Give me a hint
Stay within what a non-living model shows.
Compare my reasoning
- The comparison can support a relationship between size, SA:V and diffusion fraction.
- Agar does not reproduce living membranes or active transport.
The model can show that block size and SA:V affect the fraction reached by diffusion over a fixed time. It cannot demonstrate transport across living membranes, active transport or metabolism because agar is non-living.
Look for these in your work
- Conclusion tied to measurement
- Model limitation stated
Common mistakes
- Comparing different exposure times
- Reporting penetration distance as if it were the fraction of the block reached
- Calling an agar block a living cell
What can you explain now?
What should remain the same when comparing agar blocks of different sizes?
Compare with the explanation
Diffusion time and solution conditions
Only block size should be deliberately changed.
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Make it stick
How do block size and SA:V affect the fraction reached in an agar diffusion model, and what are its limits?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.