Name: ______Date: ______Hr: ______
Inverse Variation and Oil Spill Volume
As soon as a quantity of oil is spilled, it starts to spread. If not stopped, the oil slick can cover a very large area. As the oil spreads, the depth of the oil slick decreases. In the following exploration, you investigate the relationship between the depth of a spill and the area it covers.
Obtain these materials from your teacher:
Cup of water (about 200 mL)
Cylindrical Containers of different widths (take only a few at a time and then return)
Data Collection:
You are going to simulate an actual oil spill using your water and different containers.
1. Obtain your first container from your teacher. Carefully measure the diameter of the base of the container to the nearest 10th of a centimeter. Please measure the inside diameter of the container, not the outside diameter. Ignore the thickness of the container. Put this measurement in the chart.
2. Now calculate the area of the base of the container. Fill this into the chart.
3. Pour your water into the container. Measure the height of the water from the bottom of the inside of the jar (ignore the thickness of the bottom) to the nearest 10th of a centimeter. Record this value in the chart.
4. Now calculate the volume of your water in the container by multiplying base area times height of the water!! If you calculate correctly, your water volume should always be the same, regardless of your container.
5. Repeat this process with a different container until you have completed the chart below.
Container letter / Diameter (cm) / Area of Base (cm2) / Height of Water (cm) / Volume of Water (cm3)A
B
C
D
E
F
G
H
6. Now go to a classroom computer and open the Graphical Analysis program.
7. Double click the top of the x-column and re-name it base area (incm2).
8. Double click the top of the y-column and re-name it height (in cm).
9. Fill in the values from your chart and have the computer make a graph of height (y-axis) vs. base area (x-axis).
10. Have the computer put an inverse fit through your graph to get the equation of thegraph.
11. Print up your graph, with the computer’s inverse fit. Under your graph, write the inverse equation the computer gave you in the form y = k/x.
Data Analysis:
1. In your equation, what do the x and y variables represent (which is base area and which is height)?
x: ______y:______
2. In a few complete sentences, explain why this makes sense as an inverse proportion rather that a direct proportion.
3. Suppose you were to use a container that had a base are of about 100 cm2. Use your graph to estimate the height of the water in your container. Circle the point on your graph.
4. Suppose you had a water height of 10 cm. Use your graph to estimate the base area of your container. Put a square around the point on your graph.
5. Suppose you were to use a container that had a base are of about 100 cm2. Use your equation to find the height of the water in your container. Show your work. How does your value compare with your answer to #3 above.
6. Find the equations of at least 2 other groups and write them below:
Group 1:
Group 2:
7. Were the equations from the other groups exactly the same as yours? How do you know? Why do you think this might be true?