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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 students with a 'hands-on' activity that simulates the changing relationship of Surface Areas -to- Volume for a growing cell.

Background
Pairs of students are given duplicated copies of the Cubic Cell Models on heavy, colored paper (Fig.1). The four cell models are then cut out, folded, and glued together by the students. 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. If one unit equals 1.3 cm or less, all four cutouts will fit on one 8.5 -by- 11 inch page. After assembling the cell models, students fill each cell with fine sand. The sand is kept level with the open top of each cell.
 * Making Model Cells**

Project
By analyzing the four sand-filled cubic models, students can find answers to many questions about cell growth such as the following. (Answers are contained in the parentheses.) 1. Give the formula for computing the following data about the cell models when the length of one side equals "s" : Area of one face (A = s2); Total surface area of a cell (A = 6 x s2); Volume of a cell (V = s3); and Distance from the center of cell to center of each wall (D = s/2). 2. Compute the data above for each cell. The smallest cell has s =1 unit, and the largest cell has s = 4 units (Table 1). 3. Using a scale, find the weight of each sand-filled cell in grams (Table 1). 4. Compute the Surface Area -to- Volume Ratio and Surface Area -to- Weight Ratio for each cell (Table 2). 5. 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 ? (Total Surface Area). 6. 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). 7. As the cell grows larger and gets more cell content, will it need more or less cell membrane to survive ? (The cell needs more membrane in order to provide greater area for intake of oxygen and food and release of waste.) 8. As the cell grows larger, does the Total Surface Area -to- Volume Ratio get larger, smaller, or remain the same ? (The ratio decreases from 6 to 1.5) 9. As the cell grows larger, what happens to the Total Surface Area -to- Weight Ratio ? (The ratio decreases from 1.5 to 0.37). 10. Why can't cells survive when the Total Surface Area -to- Volume ratio becomes too small ? (The greater cell content needs more oxygen and food than the membrane can take in and produces more waste than the membrane can release.) 11. Which size cell has the greatest Total Surface Area -to- Volume Ratio ? (The smallest cell.) 12. Which size cell has the greatest chance of survival ? (The smallest cell.) 13. What can cells do to increase their Total Surface Area -to- Volume Ratio ? (Divide.) 14. How many s = 1 unit cells would fit into an s = 3 unit cell ? (27). 15. Which has more Total Surface Area, one s = 3 cell or 27 s = 1 cells ? (27 s = 1 cells.) Have students stack 27 s=1 cells inside a s=3 cell.
 * Comparing Cell Sizes**

code Cell Size | Area of |Total Surface|Volume of  |Distance from |Weight of Cell s Units | One Face | Area        | Cube Cell |Center to Edge|Filled w/Sand
 * Table 1. Measurements of Cube Cell Models**

=
====================================================================   1         1            6            1             0.5           ~  4    grams 2        4           24            8             1.0           ~  32    3         9           54            27            1.5           ~  1    4        16           96            64            2.0           ~  256

code code Cell Size     |        Total Surface Area         |      Total Surface Area Units         |         -to-  Volume  Ratio       |      -to-  Weight  Ratio
 * Table 2. Ratios of Cube Cell Models**

=
====================================================================        1                    6 / 1  =  6  =  6:1          6 / 4  =  1.5         2                   24 / 8  = 3   =  3:1          24 / 32  =  0.75         3                   54 / 27  =  2  =  2:1         54 / 108  =  0.5         4                   96 / 64  =  1.5  =  3:2       96 / 256  =  0.375

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Figure for the containers: