Download Why don`t Cells Grow Indefinitely Lab

Chapter 5 Lab: Why don’t Cells Grow Indefinitely?
Background:
Many cells grow until they reach a certain size and then divide. Why don’t cells grow indefinitely, until they become the
size of basketballs? What problems arise when a cell grows large? Why does a cell divide into two smaller cells when it
reaches a certain size? These are all questions that scientists have attempted to resolve.
Cell division is a necessary part of the life of any multicellular organism and allows for growth, repair, and formation of
cells for reproduction. Growth of an organism occurs mainly by an increase in the number of cells rather than by the
enlargement of individual cells. This process seems to be controlled by simple physical laws.
Objectives:
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Make a hypothesis that describes the relationship among surface area, volume and mass of a cell.
Determine the relationship between surface area and volume of a model cell.
Determine the relationship between surface area and mass of a model cell.
Apply these mathematical relationships to living cells.
Materials:
3 cell models
Balance
Sand
Small Scoop
Procedure
1. Cut out the three cell models. Fold and glue together all sides of each model. You
will have three structures that resemble open boxes, as in Figure 1. Imagine that
each cell model has a sixth side and is a closed box. These models represent a cell at
three different stages of growth. The youngest stage in growth is represented by
the model that is 1 unit to a side. The latest stage in growth is represented by the
model that is 4 units to a side.
2. Make a hypothesis that predicts what will happen to the surface area-to-volume ratio and the surface area-tomass ratio as the cell grows larger. The ratio can increase, decrease, or stay the same. Write your hypothesis in
the space provided below.
Hypothesis: _______________________________________________________________________________________
__________________________________________________________________________________________________
__________________________________________________________________________________________________
3.
4.
5.
6.
7.
8.
Examine Table 1. Next to the row marked Formulas, write in the mathematical formulas that can be used to
calculate the value described in the heading of each column.
Use your formulas to calculate values (except for the last column) for each of the three cell models. Record your
values in Table 1.
Fill each cell with sand, using the scoop.
Determine the mass of each sand-filled model cell by using a balance. Record the masses in the last column of
Table 1.
Calculate the ratio of total surface area to volume for each model cell. To do this, divide the cell’s total surface
area by its volume. Place your answers in Table 2.
Calculate the ratio of total surface area to mass for each model cell. To do this, divide the cell’s total surface
area by its mass. Place your answers in Table 2.
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Data and Observations
Table 1:
Measurements of Cell Models
Formulas
Cell size (length
of one side)
Area of one face
(cm2)
Total surface
area of a cell
(cm2)
Volume of a cell
(cm3)
Distance from
center to edge
(cm)
Mass of cell (g)
1
2
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Table 2:
Cell size (Length of one
side)
1
2
4
Ratios of Cell-Model Measurements
Total surface area to Volume
Total Surface area to mass
Analysis
1.
Anything that the cell takes in, such as oxygen or food, or lets out, such as carbon dioxide, must pass through
the cell membrane. Which of the measurements of your model cell best represents the surface are of the cell
membrane? _________________________________________________________________________________
___________________________________________________________________________________________
2. The cell contents, including the nucleus and the cytoplasm, use food and oxygen and produce wastes. Which
two measurements best represent the contents of one of your model cells? _____________________________
___________________________________________________________________________________________
3. As a cell grows larger and accumulates more contents, will it need more or less cell membrane to survive?
Explain your answer. __________________________________________________________________________
___________________________________________________________________________________________
4. As a cell grows larger, does the surface area-to-volume ratio get larger, get smaller, or remain the same?
__________________________________________________________________________________________
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5. As a cell grows larger, what happens to the surface area-to-mass ratio? _________________________________
6. Which cell model has the greatest surface area-to-volume and surface area-to-mass ratios?
___________________________________________________________________________________________
7. Why can cells not survive when the surface area-to-volume ratio and surface area-to-mass ratio become too
small? ______________________________________________________________________________________
a. Which cell model then has the greatest chance of survival? _____________________________________
8.
How many cells with s=1 would fit into a cell with s=3? ______________________________________________
9. Which has more total surface area, one cell with s=3 or 27 cells, each with s=1? ___________________________
10. How can the surface area-to-volume and surface area-to-mass ratios be increased in a large cell?
___________________________________________________________________________________________
11. As the length of a side doubles in a cell, what happens to the distance that nutrients must travel to reach the
center of the cell? ____________________________________________________________________________
CER: Analyze the question and your hypothesis for what happens to surface area-to-volume ratio and the surface areato-mass ratio as the cell grows larger.
Claim: ______________________________________________________________________________________
Evidence: ___________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
Reasoning: __________________________________________________________________________________
___________________________________________________________________________________________
___________________________________________________________________________________________
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Homework: What determines the size of a cell?
Intro: Sometimes bigger is better; closet size and bank account balances might come to mind. What about
cells? Does having large cells make an organism better or give an advantage? If so, why do cells divide instead
of continue to grow? What advantages might there be for smaller cells?
Model 1 – Investigating Cell Size
1. Label the following organelles in Cell B: Cell membrane, cytoplasm, endoplasmic reticulum,
Golgi apparatus, mitochondria, nucleus, vacuole(s)
2. Are the two cells in Model 1 plant or animal cells? Explain your answer.
3. In Model 1, compare Cell A to Cell B and then circle your answer.
Which cell has a larger surface area (more cell membrane)?
Cell A or Cell B
Which cell has more channels in the cell membrane to transport molecules
(such as water, oxygen, nutrients and waste) into and out of the cell?
Cell A or Cell B
Which cell has a larger volume?
Cell A or Cell B
Which cell has more mitochondria?
Cell A or Cell B
In which cell would it take longer for a glucose molecule entering the cell membrane to reach a mitochondrion?
Cell A or Cell B
In which cell would it take longer for carbon dioxide molecule leaving a mitochondrion to reach the cell membrane?
Cell A or Cell B
4. Explain the consequences for a cell if there were not enough channels in the cell membrane
for bringing in nutrients and removing waste.
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5. Explain why one cell might need more mitochondria than another.
6. Considering your answers to #3-5, Is bigger always better for a cell? Explain your answer.
Model 2 – Comparing Shapes
Length
Cubes
1.0 cm
2.0 cm
4.0 cm
2.0 cm
4.0 cm
Surface Area (= 6·Length2)
Volume (= Length3)
Surface Area
Volume
Spheres
Diameter
1.0 cm
Surface Area (= 4π·radius2)
Volume (= 4/3 π·radius3)
Surface Area
Volume
7. Calculate the surface area and volume for each of the cubes and spheres. Record your answers in the table.
8. Describe the change in the surface area of the cube (or circle) each time the length of the side (or diameter) doubles.
9. Describe the change in the volume of the cube (or circle) each time the length of the side (or diameter) doubles.
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10. As a shape gets larger, which increases faster? Surface Area or Volume
Circle your answer.
11. Calculate the surface area-to-volume ratio for each of the cubes and spheres. Record your answers in the table.
12. Describe the change in surface area-to-volume ratio as the size of the shapes increases.
13. Considering your answer to #6, is it more desirable for a cell to have a small or large surface area-to-volume ratio?
Explain in terms of cell functions.
14. A cylinder with a diameter of 1 cm and a length of 3.5 cm has a surface area of 12.57 cm2 and a volume of 2.75 cm3.
How do the surface area, volume and surface area-to-volume ratio of this cylinder compare to the 2 cm diameter sphere?
15. Why would a cylindrical shape be more efficient for large cells like nerve or muscle cells?
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