LIFE’S DIFFICULTIES … TO BE BIG OR SMALL?
and ….
MODELING SURFACE AREA TO VOLUME RATIO AND
CONSEQUENT LIMITS TO CELL SIZE
Abstract
Why can't cells continue to grow larger and larger to become giant cells, like a blob? Why are most
cells, whether from an elephant or an earthworm, microscopic in size? What happens when a cell
grows larger and what causes it to divide into two smaller cells rather than growing infinitely larger?
This investigation provides a 'hands-on' activity that simulates the changing relationship of Surface
Areas-to-Volume for a growing cell.
Materials
Each group needs:
i)
ii)
iii)
iv)
Cubic cell models template
Scissors and glue
Sand
Access to a simple digital balance
Making Model Cells
The Cubic Cell Models have been copied onto coloured card (Fig.1). Cut out the four cell models from
the template and then fold and glue them together. The models represent one cube-shaped cell at
increasing stages of growth. The smallest stage represented is 1 Unit long on a side; the largest stage is
4 Units on a side. Fill each cell with fine sand. The sand should be level with the open top of each cell.
Data, analysis and conclusions - Comparing Cell Sizes
By analyzing the four sand-filled cubic models, you can find answers to many questions about cell
growth such as the following:
1.
Try to give the formula for computing the following data about the cell models when the length
of one side equals "s" :

Area of one face: s^2

Total surface area of a cell: surface area = (Length X Width) X 6 sides

Volume of a cell: volume = length X width X height

Distance from the centre of cell to centre of each wall: s/2
2.






This is the data you will need to analyse and from which to make conclusions:
Cell size (s units)
Surface area of one face
Total surface area of cell
Volume of cell
Distance from the centre to the edge
Weight of cell when filled with sand
Use this table to record your data and calculations:
Total
surface
area of cell
(mm2)
6
Volume of
cell
(mm3)
1
Surface
area of one
face
(mm2)
1
2
4
3
4
Size
(s units)
Cell
1
Distance
from centre
of cell to
edge (mm)
0.5
Weight of
cell when
filled with
sand (gms)
1.9
16
8
1
11.6
9
54
27
1.5
39.8
16
96
64
2
99.2
1
2
3
4
3.
Calculate the data above for each cell and complete the table. The smallest cell has s =1 unit,
and the largest cell has s = 4 units.
4.
Using a balance, find the weight of each sand-filled cell in grams and record this.
5.
Now you need to complete another table with the following calculated data:



Cell size in s units
Surface area : volume ratio
Surface area : weight (of sand) ratio
Cell 1 - 1 Units
Cell 2 - 2 Units
Cell 3 - 3 Units
Cell 4 - 4 Units
Surface area : Volume ratio
Surface area : Weight ratio
1:1
1:1.9
4:8
2:11.6
9:27
3:39.8
16:64
4:99.2
6.
Anything that the cell takes in, like oxygen and food, or lets out, such as carbon dioxide, must
go through the cell membrane. Which measurement of the cells best represents how much cell
membrane the models have?
-The surface area.
7.
The cell contents, nucleus and cytoplasm, use the oxygen and food while producing the waste.
Which two measurements best represent the cell content?
-Weight & Volume.
8.
As the cell grows larger and gets more cell content, will it need more or less cell membrane to
survive?
-It needs more cell membrane.
9.
As the cell grows larger, does the Total Surface Area-to-Volume Ratio get larger, smaller, or
remain the same?
-Smaller
10.
As the cell grows larger, what happens to the Total Surface Area-to-Weight Ratio?
-It decreases.
11.
Why can't cells survive when the Total Surface Area-to-Volume ratio becomes too small?
-When a cell has a smaller Total Surface Area-to-Volume ratio, they won’t be able to let in or
produce any gasses/heat.
12.
Which size cell has the greatest Total Surface Area-to-Volume Ratio?
-Cell with a size of 1 has a greater Total Surface area to Volume Ratio.
13.
Which size cell has the greatest chance of survival?
-The bigger the surface area, the better the gas exchanges. So in this case, cell 3.
14.
What can cells do to increase their Total Surface Area-to-Volume Ratio?
-To increase the surface area: volume ratio, the cell can either:
1. Increase its surface area or
2. Decrease its volume
15.
How many s = 1 unit cells would fit into an s = 3 unit cell?
27 s=1 unit cells fit into an s=3 unit cell.