IB Modeling Cell Surface Area to Volume Ratios
A cell’s surface areatovolume ratio affects the amount of material that can diffuse across the membrane and throughout the cell. You will make cell models to determine how this ratio changes as cell size increases and this affects the rate of diffusion.
Question:
How does the surface areatovolume ratio of a cell affect the rate of diffusion?
Materials:
 Plastic knife
 Phenolphthalein agar
 metric ruler
 250mL beaker
 100mL graduated cylinder
 100 mL sodium hydroxide solution
 Timer
 Plastic spoon
 Paper towel
Procedure:
 Make two model cells by using the knife to cut two cubes from the phenolphthalein agar. Cell A should be 2u cm on each side and Cell B 1 cm on each side. Use a ruler to make exact measurements.
 Complete the following in Table 1.
 Calculate the area of one side of each cell. Calculate the total surface area of each cell. Actually do this for the measurements of your cells, not just the given 2 or 1 cm values.
 Calculate the volume of each cell.
 Calculate the ratio of surface area to volume for each cell.
 Read the remainder of the instructions. Before proceeding, write a hypothesis of what you expect to occur (comparing the two cells) below:
 Add 80ml of distilled water and 15 drops of ammonia to a 100ml beaker; the water must cover the cells.
 Put the model cells in the beaker (cubes need to be completely submerged) when directed to do so. Soak the cells in solution for 15 minutes.
 Remove the cells from the solution and pat them dry on a paper towel.
 Use the knife to cut each in half. Measure the distance (in mm) from the edge of the cell to the inner edge of the pink line; this will be used to show the rate (distance of diffusion over time). This shows how far the ammonia has diffused. Record your results in your data table; if pink has diffused the entire cell still only measure diffused distance to the halfway point of the cell.
 Add your data to this form for entire class analysis
Data Collection & Processing
Table 1. Calculations of Cell Size for Cell A & Cell B
Cell  Area of One Side (cm2)  Total Surface Area (cm2)  Volume of Cell (cm3)  Surface Area to Volume Ratio  Distance Diffused by Ammonia (mm) 
A (2 cm) 





B (1 cm) 





Table 2. Ammonia Diffusion Raw Data for Entire Class
Group Members  Cell A (3 mm)  Cell B (1 cm) 







































Mean: 


Standard Deviation: 


Table 3. Qualitative Data for Diffusion for Cell A & Cell B
Cell A (2 cm)  Cell B (1 cm) 


Data Collection & Processing: Complete the following data processing either below (you can use the “Insert” “Equation” function from the tool bar above or write out on a piece of paper and upload below as an image file). Each process should be clearly labeled and include a sample calculation.
 Calculate the mean and standard deviation for each cell type for the whole class data found here.
 Conduct a TTest for the comparison of the distance of diffusion to see if there is a statistical difference between Cell A and Cell B; be sure to include a null hypothesis and summary statement.
Conclusion & Evaluation:
 Restate the hypothesis and question of the experiment.
 Confirm or deny the hypothesis using data and statistical analysis.
 Describe how does the surface areatovolume ratio change as cell size increases (Use data and your statistical calculations to answer this question).
 Explain how the observed outcomes (diffusion rates for different surface areatovolume ratios) relate to the diffusion of material throughout a cell and its size.
 Analyze why a cell’s surface areatovolume ratio would affect its ability to be efficient.
 Describe limitations to the procedure of lab (not your human error, focus on what problems were present with the procedural that limited the ability to collect quality data).
 Suggest realistic improvements and modifications to address question 6 .
Assessment:
IB Mark  Analysis Descriptor 
56   The report includes sufficient relevant quantitative and qualitative raw data that could support a detailed and valid conclusion to the research question.
 Appropriate and sufficient data processing is carried out with the accuracy required to enable a conclusion to the research question to be drawn that is fully consistent with the experimental data.
 The report shows evidence of full and appropriate consideration of the impact of measurement uncertainty on the analysis.
 The processed data is correctly interpreted so that a completely valid and detailed conclusion to the research question can be deduced.

34   The report includes relevant but incomplete quantitative and qualitative raw data that could support a simple or partially valid conclusion to the research question
 Appropriate and sufficient data processing is carried out that could lead to a broadly valid conclusion but there are significant inaccuracies and inconsistencies in the processing
 The report shows evidence of some consideration of the impact of measurement uncertainty on the analysis
 The processed data is interpreted so that a broadly valid but incomplete or limited conclusion to the research question can be deduced

12   The report includes insufficient relevant raw data to support a valid conclusion to the research question
 Some basic data processing is carried out but is either too inaccurate or too insufficient to lead to a valid conclusion
 The report shows evidence of little consideration of the impact of measurement uncertainty on the analysis
 The processed data is incorrectly or insufficiently interpreted so that the conclusion is invalid or very incomplete

0  The student’s report does not reach a standard described by the descriptors above. 
A full explanation of the lab standard rubric can be found here