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 squared..........................................................................................................

Total surface area of a cell: 6 s squared...................................................................................

Volume of a cell: s cubed ......................................................................................................

Distance from the centre of cell to centre of each wall: s divided by 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)
1.7
24
8
1
13.0
9
54
27
1.5
43.6
16
96
64
2
106/3
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
Surface area : Volume ratio
Cell 1 - 1 Units
Cell 2 - 2 Units
Cell 3 - 3 Units
Cell 4 - 4 Units
Surface area : Weight ratio
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 cell membrane. It covers the surface of a unit like the cell membrane covers the surface if
the cell. This allows nutrients to be let out.
7.
The cell contents, nucleus and cytoplasm, use the oxygen and food while producing the waste.
Which two measurements best represent the cell content?
Volume and weight. The volume it related to how much space is contained inside the unit. And
the weight is a measurement related to the unit mass.
8.
As the cell grows larger and gets more cell content, will it need more or less cell membrane to
survive?
It will need more cell membrane to be able to survive because there is a grater surface area to
cover. But the total surface area will decrease. So even though a bigger cell has more cell
membrane, it doesn’t have as much cell membrane as a group of smaller cells, which have the
same amount of volume.
9.
As the cell grows larger, does the Total Surface Area-to-Volume Ratio get larger, smaller, or
remain the same?
When the cell grows, the Total Surface Area decreases.
10.
As the cell grows larger, what happens to the Total Surface Area-to-Weight Ratio?
It also decreases.
11.
Why can't cells survive when the Total Surface Area-to-Volume ratio becomes too small?
Cells need a larger surface area because it passes through their membrane. Here they expel the
remaining waste and they absorb nutrients. In a large cell the waste that has been expelled and
also the nutrients which needed to survive would be too much for the cell membrane to take in.
12.
Which size cell has the greatest Total Surface Area-to-Volume Ratio?
The cell with a size of unit 1.
13.
Which size cell has the greatest chance of survival?
Also the cell with a size of unit 1 because it has the gratest total surface area to volume ratio
and also the gratest total surface area to weight ratio. If the surface area to volume ratio is small, the
cell would have trouble absorbing nutrients and expelling waste for its size. So they have to have a
bigger surface area to volume ratio in order to survive.
14.
What can cells do to increase their Total Surface Area-to-Volume Ratio?
They can reduce their size. For example, the smallest cell had the gratest surface area to
volume ratio.
15.
How many s = 1 unit cells would fit into an s = 3 unit cell?
27 s equals 1 unit cell would fit into an s equals 3 unit cell. But the total surface area of 27 s
equals 2 unit cells would be much bigger than that of 1 s equals 3 unit cell.