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Bio 103 - Introduction to Biology
                                 Chapter 4: A Tour of the Cell
                                       Modeling Cells: Surface to Volume

Background: Are there limits as to how large organisms can grow? Some humans are very tall but do not
grow as large as trees. Some large insects do exist but never grow to reach the sizes you might see in science
fiction films. Why? One reason is that with increasing height there is a disproportionate increase in volume (or
weight). If the height of an elephant were doubled, its weight would increase by eight times its original weight.
An elephant cannot grow larger, because its legs could not support the increase in weight.

In this activity you will examine surface area-to-volume ratios on a small scale, using some model cells. You will
use the collected data to reach some conclusions as to why this ratio might limit the size of a cell.

Objectives:
   • construct and analyze various cell models.
   • measure volume and calculate surface area.
   • calculate surface-area-to-volume ratios.
   • form conclusions about size limitations, using your data.

Materials:
   •  scissors
   •  cell model cutouts (3)
   •  poster board
   •  tape
   •  metric ruler
   •  sand
   •  funnel
   •  large graduated cylinder
   •  calculator (optional)

Preparation:
Cut out three cell models and fold each to form a three-dimensional shape. Cell dimensions should be recorded
in the table in step 1 below. Use tape where directed so that the models hold their shape.

Procedure:

                                  1.   Using the metric ruler, measure the length, width, and height dimensions
                                       of each model. Record the dimensions in a table like the one shown below.

                                         Cell      Dimensions          Surface Area   Volume         Ratio
                                                      (cm)                (cm2)        (cm3)   Surface to Volume

                                          A

                                          B

                                          C



                                  2.    Fill each model with sand. Level off the sand at the top of the model,
                                       using the ruler.




                                                               1
                                                success = preparation + execution
3.   Find the volume of sand in each model. You can do this two ways.
        a. Measure the amount of sand in each model, using a graduated cylinder. Pour the sand through the
            funnel into the graduated cylinder or a measuring cup. One millimeter = one cubic centimeter (l cm3).

        b.   Calculate the volume using the formula in step 2 of Analysis (below).


Analysis:
   1. Complete the data table by calculating the area and volume of each model. To calculate total surface area
      for each model, find the area of each side (length x width) then multiply that number by 6. Enter the
      data in your table. Why do you need to multiply by 6?


   2.   To calculate the volume of sand, use the following formula:

                                        volume = length x width x height
                                  Record the volume of each model in your table.

   3.   Calculate the surface area-to-volume ratio for each model. Use the following formula:

                                              surface area/volume = ratio

        Record the value in your table.

   4. Which model has the largest surface area?



   5.   Which model has the largest volume?



   6. Which model has the largest ratio?



   7. To maintain life, materials must be able to move into and out of a cell. What might be the advantage of
      having a large surface area?




   8. What might be the disadvantage of having a large volume?




                                                            2
                                             success = preparation + execution

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C04 Cell Surface Area

  • 1. Bio 103 - Introduction to Biology Chapter 4: A Tour of the Cell Modeling Cells: Surface to Volume Background: Are there limits as to how large organisms can grow? Some humans are very tall but do not grow as large as trees. Some large insects do exist but never grow to reach the sizes you might see in science fiction films. Why? One reason is that with increasing height there is a disproportionate increase in volume (or weight). If the height of an elephant were doubled, its weight would increase by eight times its original weight. An elephant cannot grow larger, because its legs could not support the increase in weight. In this activity you will examine surface area-to-volume ratios on a small scale, using some model cells. You will use the collected data to reach some conclusions as to why this ratio might limit the size of a cell. Objectives: • construct and analyze various cell models. • measure volume and calculate surface area. • calculate surface-area-to-volume ratios. • form conclusions about size limitations, using your data. Materials: • scissors • cell model cutouts (3) • poster board • tape • metric ruler • sand • funnel • large graduated cylinder • calculator (optional) Preparation: Cut out three cell models and fold each to form a three-dimensional shape. Cell dimensions should be recorded in the table in step 1 below. Use tape where directed so that the models hold their shape. Procedure: 1. Using the metric ruler, measure the length, width, and height dimensions of each model. Record the dimensions in a table like the one shown below. Cell Dimensions Surface Area Volume Ratio (cm) (cm2) (cm3) Surface to Volume A B C 2. Fill each model with sand. Level off the sand at the top of the model, using the ruler. 1 success = preparation + execution
  • 2. 3. Find the volume of sand in each model. You can do this two ways. a. Measure the amount of sand in each model, using a graduated cylinder. Pour the sand through the funnel into the graduated cylinder or a measuring cup. One millimeter = one cubic centimeter (l cm3). b. Calculate the volume using the formula in step 2 of Analysis (below). Analysis: 1. Complete the data table by calculating the area and volume of each model. To calculate total surface area for each model, find the area of each side (length x width) then multiply that number by 6. Enter the data in your table. Why do you need to multiply by 6? 2. To calculate the volume of sand, use the following formula: volume = length x width x height Record the volume of each model in your table. 3. Calculate the surface area-to-volume ratio for each model. Use the following formula: surface area/volume = ratio Record the value in your table. 4. Which model has the largest surface area? 5. Which model has the largest volume? 6. Which model has the largest ratio? 7. To maintain life, materials must be able to move into and out of a cell. What might be the advantage of having a large surface area? 8. What might be the disadvantage of having a large volume? 2 success = preparation + execution