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Grade: Senior
Subject: Science

#2518. Surface to Volume Ratios

Science, level: Senior
Posted Sat Nov 9 11:02:02 PST 2002 by John Matyasovsky (
Norwin High School, North Huntingdon, PA USA
Materials Required: Listed in Lesson
Activity Time: 2-43 min periods 1 hour prep
Concepts Taught: Surface Area to Volume Ratios. Cell Size

Cell Size: Surface to Volume Ratios
Chapter 5: Cell Structure and Function

The purpose of this laboratory experiment is to measure the rate of diffusion in agar and to calculate the surface area to volume ratios of varying cell sizes.

Background Information
In this lab you will construct a simple model that will allow you to examine the relationship between cell structure and cell function. The structure of a cell relates to its function. The difference in the structure of a nerve cell and a skin cell, for example, reflects the difference in their functions.

Increasing cell size affects passive diffusion-the movement of small molecules across the cell membrane from regions of higher concentrations to regions of lower concentration. In this lab, you will see how increasing cell size imposes certain restrictions on passive diffusion. This will be accomplished by modeling the relationship between diffusion and the ratio of a cell's surface area to its volume.


Surgical Gloves
Agar block containing phenothalein
Plastic spatula or spoon
Glass plate
Metric ruler
Scalpel or single edge razor blade
250-mL Beaker
100mL 0.2 hydrochloric acid
4-6 Sheets of white paper
Latex gloves should be worn at all times during this laboratory activity.

1. Note the diagram below showing how to cut the agar blocks. Use a spatula or a spoon to place the blocks on a glass plate. Cut the agar block as shown. Clear the cutting procedure with your teacher BEFORE YOU START. It is imperative that you do not touch the blocks with bare hands.

2. CAREFULLY place all four blocks into the beaker. Make sure that none of the edges touch. Add enough dilute hydrochloric acid to cover the cubes completely. Why is it necessary that none of the edges of the blocks are nicked or damaged? How would skew your results?
3. Record the exact time on a piece of paper.
4. Gently lift each block to be sure that all surfaces contact the acid. Gently swirl the beaker occasionally to promote contact with fresh acid.
5. At your teacher's instruction, carefully lift out Block 4. Place the block on a white sheet of paper-for color comparison.
6. Record the time on a sheet of paper.
7. Cut Block 4 down the center with the CLEANED razor blade or scalpel. Work quickly but carefully. After the cut, clean the razor blade or scalpel.
8. Repeat steps 5 and 7 for each of the remaining blocks-from smallest to the largest. Why is it necessary to remove the blocks in this specific order?
9. Measure in millimeters the distance the acid has penetrated into each block, and record on the attached CLASS DATA CHART. Is the distance the same from all edges of the same block?
10. Record the elapsed time in minutes on the CLASS DATA CHART.
11. Calculate the rate of diffusion as millimeters per minute and record in the CALCULATION SHEET. Add you data to the CLASS DATA CHART and record the data from the other teams on your chart.

Data and Observations


Questions and Conclusions
In the space provided below, answer the underlined questions in the procedure. Use complete sentences, proper grammar, and scientific terms.

Why is it necessary that none of the edges of the blocks are nicked or damaged? How would skew your results?

Why is it necessary to remove the blocks in this specific order?

Is the distance the same from all edges of the same block?

Answer the following the questions using complete sentences, proper grammar, and scientific terms.

1. What was the average rate of diffusion for each block?

2. According to your data, how does the surface area to volume ration relate to the rate of diffusion?

3. Using the distance that the acid traveled into the cube, calculate the percentage of the volume of Blocks 1 and 2 that exhibited diffusion. Accomplish this by calculating the volume where the acid did not reach, and subtract that from the total volume.

4. If a cell has a small surface area-to-volume ratio, how well do you think molecules can pass in and out of it? Relate this to respiration and excretion at the cellular level.

Class Data Chart

Class Data -Rate of diffusion
Block 1 Block 2 Block 3 Block 4
Distance (mm) Time (min) Rate (mm/min) Distance (mm) Time (min) Rate (mm/min) Distance (mm) Time (min) Rate (mm/min) Distance (mm) Time (min) Rate (mm/min)

Surface Area / Volume Ratio
Length Width Height Surface Area Volume Ratio
Block 1 30 mm
Block 2 20 mm
Block 3 10 mm
Block 4 5 mm

Calculation Sheet

Use the following equations to help with your laboratory exercise. Show the mathematical work for at least ONE of each of the types of calculations.

Surface Area = 6 x L X W X H
Volume = L X W X H
Ratio = Surface Area / Volume
% of diffusion = total volume - volume not reached by acid

Use the space below for your calculations.

Teacher Notes and Preparation Information

The agar blocks

Homogenization medium
30-mL liquid dish soap or shampoo
8.8-g Sodium chloride
4.4-g Sodium citrate
0.3-g EDTA
1-L Distilled water

P Place the ethanol in a freezer overnight in a bottle not completely full with a loose cap.

The materials list below is enough for a class of 30 students.

Homogenization medium
Boiling Water Bath
95-100% Ethanol
60 Latex gloves
15 Medium-sized onions
15 Cutting boards and scalpels
30, 250-mL Beakers
15 Rulers, Metric
Ice Bucket
1 Package of Cheese cloth
60, 10-mL Test tube
30 Glass stirring rods
15 Grease pencils
15 Stopwatches