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Copland CollegeYear 11/12 - Science for Life |
Science for Life - Surface Area to Volume Ratio Your body is made up of billions of cells. Why is this the case? Why aren't organisms made up of a single cell? You sometimes read how a baby had to be rescued from a car on a hot day. Animals such as small rodents have to eat throughout the day in order to stay alive. How can these phenomena be explained mathematically. The answer to each of these questions lies in the concept of surface area to volume ratio. As an object changes size the amount of surface area available to each unit of volume changes. In the activity that you have carried out so far you placed some potato into an iodine solution. The solution turned the potato black as the iodine reacted with the starch. The question we need to ask is what difference, if any, exists between our smallest potato cube and the largest cube in terms of which is more efficient in absorbing the iodine. The iodine is really acting like nutrients used by animal or plant cells. Our potato cube is the animal or plant cell. Being cubic in shape makes calculations a little easier for us. Of course most cells are anything but cubic. For this activity you will use the program Excel. As you probably already know Excel is very good in doing calculations and manipulations on numbers and data. It is also very good for graphs. Task #1: Open Excel. Set up a spreadsheet that looks similar the following.
Your task now is to write a formula that will allow you to calculate the surface area of the each cube, the volume of that cube and the SA to Volume ratio. The general formula for surface area of a cube is side multiplied by side all multiplied by 6. If you have not written a formula in Excel before type the following into cell B4, =(A4*A4)*6 This formula is copied and pasted down the column. In a similar fashion write a formula in cell C4 to calculate the each cube's volume. This formula is of course side multiplied by side multiplied by side, or side cubed. Write the following formula into cell C4 =A4^3 This formula is copied and pasted down the column. Our last formula will allow us to calculate the surface area to volume ratio. Into cell D4 type the following =B4/C4 This formula is copied and pasted down the column. Graphing the data. We will now create a X-Y scatter graph plotting surface area/volume on the vertical axis and length of the cube side on the horizontal (X) axis. To do this
in Excel you will need to select columns A and D. As these are non
adjacent columns you will need to firstly select the numbers and column
heading in column A then whilst
holding down the Ctrl key select the numbers and column heading in column D.
Choose the
When the next dialog box occurs click Next and then type the titles as shown below.
Click the Legend tab and uncheck the Show Legend dialog box.
Finally click next and after choosing the location of your graph you should generate a graph that looks similar to the following.
Task #2. Your next activity is to determine the percentage of the volume of each cube that has turned black as the iodine solution diffused into it. To do this we will again use our spreadsheet. You should have data from last week's experiment and data that has been collected from an experiment started today. Set up a spreadsheet that looks similar to the following. Choose Sheet 2 of the original spreadsheet. Don't forget to save your work frequently. For the two sets of data you will need to duplicate the spreadsheet. One below the other to allow you to cope with the two sets of data.
Make sure you print your spreadsheets. These must then be pasted into your science book. Questions: Answer the questions from the sheet titled Relationship of Surface Area to Volume and Cell Size This sheet may have already been pasted into your workbook.
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icon from the menu
bar. When the dialog box appears choose the X-Y Scatter Graph option.
See below.
