Cells and the efficiency of the supply and removal of soluble
substances
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Partners:
Date:
Intended learning outcomes
This activity has been designed to enable you to:
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develop an understanding of the concepts of surface area and volume
recognise how the surface area to volume ratio (SA:V) of cells and objects of various shapes can
differ
comprehend how the relationship between the area and the volume of a cell affects the efficiency of
supply of substances to and removal of wastes from it
apply SA:V ratio considerations to biological situations.
Introduction
Human red blood cells have a diameter of about 7 µm. More than 100 red blood cells could be lined up across
a distance of one millimeter. Even the largest human cell, an egg cell, is only about 200 µm in diameter.
To examine cells, the human eye must be aided by one of various kinds of microscope. Other kinds of
organism also contain microscopic cells. Plant cells vary from 10 to 100 µm in diameter. Bacterial cells are
comparatively smaller. For example, the pneumonia-causing bacterium, Diplococcus pneumoniae, comprises
a single cell just 0.1 µm in diameter.
Why are cells so small? Is cell size limited in some way? Why aren’t some cells the size of elephants?
Reaching answers to these questions can be helped in part by considering the concepts of
surface area (SA ) , volume (V) and surface area to volume ratio (SA:V).
The surface area of an object is a measure of its exposed outer surface. We are very aware of this concept if
we have to paint or polish a surface — the larger the surface, the longer time the task will take. Area is
commonly expressed in units such as square centimetres (cm 2) or square metres (m 2).
The volume of an object refers to the space taken up by the object. The basic unit of measurement of volume
is the litre (L). Volume of liquid matter is commonly expressed in units such as litres (L) or millilitres (mL). For
example, the blood of an average adult female occupies a volume of about 4.5 to 5.5 L, while that of an
average adult male occupies a volume in the range of 5 to 6 L. The volume of solid matter, such as the human
brain, is sometimes expressed in cubic centimetres (cm 3). ( 1 cm3 is equivalent to 1 mL.)
The relationship between the surface area of an object and the space taken up by the object is a number
known as the surface area to volume (SA:V) ratio. This ratio is obtained by dividing the surface area by the
volume. So, a cube with a surface area of 24 cm 2 and a volume of 8 cm 3 has a SA:V ratio of 3, that is 24/8. A
ratio is simply a number and it has no units.
Knowing the SA:V ratio allows you to identify how many units of surface area are available for each unit of
volume. In the case of a cell, the higher the SA:V ratio, the more units of surface are available to take up
material to supply its internal contents or to allow wastes to be expelled.
Note:
In the International System (SI system), the unit of volume is based on metric volumes such as the cubic centimetre (cm 3)
and the cubic decimetre (dm3). The litre (L) is another unit of volume that is accepted and in use, but is not an SI unit. The
relationship between these units is: 1 L = 1.000 002 5 dm3, and so 1 millilitre (mL) is approximately equal to 1 cm 3. In this
activity, you will use millilitres (mL) since this will be a unit with which you are probably familiar.
The abbreviation for litre is most commonly a lower case ‘l’; however, a capital ‘L’ is acceptable. To avoid confusion with
the numeral ‘1’, this manual uses capital ‘L’.
Purpose/ AIM:
To see what relationship exists between the surface area and the volume of a body, and determine how this
relationship might influence the growth and survival of cells and organisms. To consider the additional effects
cell and organism shapes on factors associated with the survival of organisms.
To investigate surface area, volume and shape of cells we can simulate or model the cells of an organism with
cubes of agar of various set dimensions. Soluble requirements and wastes can be modelled using sulphuric
acid, the extent of movement into and out of the model cells can be modelled using phenolphthalein ( a pH
indicator which is pink in contact with alkalis and colourless in contact with acids.
Research Hypothesis:
3 example hypotheses re: surface area and volume
H1: The amount of movement (diffusion) of soluble substances into / out of cells is directly related to the total
surface area of the cell
H2: The amount of movement (diffusion) of soluble substances into / out of cells is directly related to the total
volume of the cell
H3: The amount of movement ( diffusion) of soluble substances into / out of cells is directly related to the
surface area : volume ratio of the cell
Testable- operationalized predictions:
If H1 is true- that the amount of movement of soluble substances into a cell is related to the total surface
area of a cell, then model cells (blocks of phenolphthalein / alkali /agar) with larger surface areas placed in
acid for 10 minutes will exhibit greater amounts of movement of acid into the blocks as measured by the
magnitude(%) of the block that turns colourless.
If H2 is true……..
If H3 is true-
Methodology:
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Use the spoon to place the three agar cubes in the beaker.
Add sulfuric acid until the blocks are submerged.
Record the time.
For the next 10 minutes, use the spoon to turn the blocks over frequently and gently.
Calculations
A. Surface area = (Length) x (width) x (number of surfaces)
B. Volume = (Length) x (width) x (height)
C. The ratio of Surface area to Volume (SA:V) is answer A : answer B.
D. Reduce the ratio by dividing both parts of the ratio by the smaller of the two numbers.
(Example: If the surface area is calculated to be 20 cm2, and the volume to be 5 cm3 \ the ratio of surface area to volume
would be 20: 5 The reduced ratio would be 20/5:5/5 = 4:1 )
• After ten minutes remove the agar blocks with the spoon, put them on paper toweling and blot dry.
• As soon as the 10 minutes have elapsed, and you have dried the agar blocks, take the razor blade and
slice each in half. Notice the extent of diffusion (the depth to which diffusion has occurred).
• Immediately measure in millimetres the distances across the cubical coloured area in the centre of
each block. Enter your results in the first column of Table 2
Work out the approximate volume of each coloured cube, and enter the volumes in the second column.
Complete the table. Work out the percentage of each block penetrated by the sulfuric acid.
Materials and Equipment:
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Agar-phenolphthalein-sodium hydroxide cubes:
-1 with 1 cm sides,
-1 with 2 cm sides,
-1 with 3 cm sides,
Rule graduated in mm
Sulfuric acid, 0.1 M, 100 mL
Beaker, 250 mL
Plastic spoon
Sharp razor blade
Paper towelling, approx. 20 cm
Clock
Results/Data:
Table 1: Initial dimensions of the model cells
CUBE
Surface Area
A
LxWx6
Volume
Each dimension
measured accurately
3cm
2 cm
1 cm
o.1 cm
LxWxH
Each dimension
measured accurately
Ratio SA: V
Reduced Ratio
Table 2: Results indicating the extent of movement of acid into the model cell
Dimensions of
Volume of
Volume of
Volume of
% of block
CUBE
coloured cube
Each dimension
measured accurately
coloured cube
B
whole block
A
From table 1
uncoloured
portion
A-B
uncoloured
3cm
2 cm
1 cm
o.1 cm
Discussion:
(Ql): List the agar cubes in order of size, from largest to smallest. List them in order of SA:V ratio, from
largest to smallest ratio. How do these two lists compare?
(Q2): Which has the greater surface area : a cube with 3 cm sides or a microscopic cube the size of an
onion cell?
(Q3): Which has the greater surface area in proportion to its volume?
(Q4): What happens to the SA:V ratio of a cell as it grows larger? If a cell was to divide into two equal
parts, how would the volume of each small cell compare with the one large cell? Would the surface area
change in the same proportion? Explain.
Q5): What evidence is there that sulfuric acid diffuses into the agar block? Is there any evidence that something was diffusing out of the agar blocks? Explain
(Q6): If the agar blocks were living cells and the sulfuric acid was a normal requirement
of a cell, which block would be supplied most efficiently by diffusion?
Increasing surface area
Cells vary in shape — some are long and thin, others are like flattened pancakes and
some are columnar. The surface of some cells is highly folded, forming structures known
as microvilli. Figure 1. opposite shows some hypothetical ‘cells’ that differ in shape but
have the same internal volumes.
Q7. These particular cells have identical internal volumes. Do they also have identical
external surface areas? Explain.
Q8. Microvilli and other extensions are found on various cells. What are microvilli and
what function might microvilli serve? Where might these cells occur?
Q9. The total surface area of the tiny root hairs on one mature rye plant about
1 metre high was estimated to be over 400 square metres. How does this
compare with the area of a tennis court?
Figure 1
Reducing surface area
Sleeping cats and dogs curl into a tight ball on a cold day. In hot weather, the same animals typically can be
seen sleeping stretched out. Some small hibernating mammals snuggle tightly together in underground nests.
Q10. Is the exposed surface area of the animal affected by these positions?
Q11. Which position — ball or stretched out — produces the greater exposed surface area?
Q12. Is the volume of the animal affected by these arrangements?
Q13. Which shape has the smaller SA:V ratio?
This behaviour is not related to the uptake of food into the animal or the removal of wastes from it. Suggest
a testable hypothesis that might provide an explanation for these observations.
Q14. In light of this hypothesis, what prediction would you make about perching birds in warm weather
compared with cold weather?
Conclusion:
A short concluding statement relating directly to the title and research hypothesis.
References:
J. Kinnear& M Martin in Nature of Biology VCE Units 1&2,. (Jacaranda. 5th ed 2016), Ch1 pp. 8-17
Instructions for writing up this prac
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Include the following sections in your report:
Section
Content and activities
Title
Question under investigation is the title
Introduction
Methodology
Explanation or reason for undertaking the investigation, including a clear aim, a hypothesis and/or prediction
and relevant background biological concepts
Summary that outlines the methodology used in the investigation and is authenticated by logbook entries
Identification and management of relevant risks, including the relevant health,safety and ethical guidelines
followed in the investigation
Results
Presentation of collected data/evidence in appropriate format to illustrate trends, patterns and/or relationships
Discussion
Analysis and evaluation of primary data
Identification of outliers and their subsequent treatment
Identification of limitations in data and methods, and suggested improvements
Linking of results to relevant biological concepts
Conclusion
Conclusion that provides a response to the question
References and acknowledgments
Referencing and acknowledgment of all quotations and sourced content.
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The dimensions of the coloured cube was measured accurately using a mm rule…..
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