Diffusion in Agar Cells Lab
Cell Size: Surface Area to Volume Ratio
Learning Objectives:

LO 2.6: The student is able to use calculated surface-to-volume ratios to predict which cell(s) might eliminate wastes
or procure nutrients faster by diffusion.

LO 2.7: Students will be able to explain how cell size and shape affect the overall rate of nutrient intake and the rate
of waste elimination.

LO 2.13: The student is able to explain how internal membranes and organelles contribute to cell functions.
Science Process Skills:

SP 2.2: The student can apply mathematical routines to quantities that describe natural phenomena.

SP 4.3: The student can collect data to answer a particular scientific question.

SP 5.1: The student can analyze data to identify patterns or relationships.

SP 6.2: The student can construct explanations of phenomena based on evidence produce through scientific
practices.

SP 7.2: The student can connect concepts in and across domain(s) to generalize or extrapolate in and/or across
enduring understandings and/or big ideas.
Introduction: All organisms are composed of cells. The size and shape of a cell determines how well
it can deliver nutrients to its interior. Since all cells and organisms depend upon the efficient delivery of
gases, nutrients, and other important molecules, the relationship between a cell's surface area and its
volume is an important regulating concept.
Purpose: This investigation illustrates why cells stop growing when they reach a certain size, why
virtually all cells are about the same size, and finally, how the ratio of surface area to volume affects
the way organisms have adapted to their environments!
What determines the efficiency of diffusion throughout the model “cells”? Use this question to
help formulate a hypothesis.
Materials:
Plastic spoon
Agar with 1% phenolphthalein
indicator solution
400 mL beaker
100 mL graduated cylinder
0.1 M NaOH
Paper towel(s)
Plastic knife
Metric ruler
*Remember safe laboratory techniques and to keep the lab area as neat and clean as possible.
Procedure:
1. Each group will cut three agar cubes: A 3cm cube, a 2cm cube, and a 1cm cube. CUT AS
ACCURATELY AS POSSIBLE. (This may be already completed for you.)
2. Consider other shapes for a cell besides a cube. What cell shape might increase the surface
area to volume ratio and allow for the fastest rate of diffusion? Using the plastic knife, carefully
carve out the shape your group has decided on for your model cell. Remember to consider size
and shape!
3. Pour 200mL of 0.1M sodium hydroxide solution into your 400mL beaker.
4. Immerse your 3 cubes and odd shape in the sodium hydroxide solution, noting the time.
5. Let the cubes soak for approximately 10 minutes.
6. Periodically, gently stir the solution, or turn the cubes over.
7. After 10 minutes, use a spoon or tongs to remove the cubes from the sodium hydroxide
solution.
8. Blot the with a paper towel.
9. Promptly cut each cube in half and measure the depth to which the pink color has penetrated.
Sketch each block’s cross-section.
Haut, J. (2012). Modified from “Cell Size: Surface Area to Volume Ratio” by D. Sodek and “Diffusion in Agar Cells” by Flinn
Scientific.
10. Record your measurements and sketch each cube in table 1.
11. Do the following calculations for each cube and complete the following data table:
Calculating % diffusion in each cube:
 Calculate total volume of each cube (volume = L x W x H)
 Calculate volume that did not turn pink. (That is, calculate total volume of the small portion of the
cube that did not turn pink – use the same formula L x W x H)
 Calculate volume diffused = total volume – volume not pink.
 Calculate % diffusion = Volume diffused /total volume x 100
Calculate the surface area of each cube and the surface area to volume ratio:
 Calculate the surface area of a cube = L x W x # of sides
 Calculate surface area/volume ratio.
Data:
Table 1. Measurements for Agar Cubes
Cube 1
(1 cm size)
Cube 2
(2 cm size)
Cube 3
(3 cm size)
Group Shape
(
)
Total Cube Volume (cm3)
Total Volume that was not pink (cm 3)
Sketch of cube
Volume of the diffused cube
(total volume – volume that was not
pink)
Percent Diffusion
Surface Area of Cube (cm2)
Surface Area to Volume Ratio
Post-Lab Questions: Copy and answer questions in your lab book.
1. What type of cellular transport did this investigation demonstrate?
2. Which shape was best able to transport the dye into the potato? How is this related to their
surface area and volume?
3. Using what you observed, explain why cells stop growing when they reach a certain size and
why all cells are about the same size?
4. What prediction can you make about the efficiency of a very small cell in: getting oxygen,
getting rid of wastes, keeping water in a dry environment, keeping heat in a cold environment?
5. What prediction can you make about the efficiency of a very large cell in: getting oxygen,
getting rid of wastes, keeping water in a dry environment,
keeping heat in a cold environment?
6. You have three cubes, A, B, and C. They have surface area to
volume ratios of 3:1, 5:2, and 4:1, respectively. Which of these
cubes is going to be the most effective at maximizing diffusion?
How do you know this?
7. Compare the appearance of the Northern Arctic hare (right) that
lives in a cold climate and the Desert Jackrabbit that lives in a
hot climate. Explain their appearance using the ratio of surface
area to volume. Explain the evolutionary advantage for each.
8. In many science fiction movies and books, a misguided scientist
is determined to use a device to enlarge an organism to gigantic proportions. Use what you
know about the surface area to volume ratio to explain the biological impossibility of such a
scenario.
Conclusion:
Write the conclusions you can draw from this experiment. For example, you may wish to address the
question as to why cells are so small (hint: a large cell would have a large surface area for diffusion,
but what about the volume?). You can also discuss why many cell organelles have folded membranes
as opposed to flat membranes.