1. What’s In The Bag Adapted from Dr. Margaret Niess

2. The Basic Idea Add a certain volume of water to a container measure how much the height increases.

3. Task 1 Get data to graph Total Volume vs. Height for a bottle with a constant circumference Get data to graph Total Volume vs. Height for a bottle with a changing circumference Figure out what the slope of a Total Volume vs. Height graph means

4. What would be the graph for a beaker?

5. What would be the graph for a flask?

6. What Does The Slope Mean The slope is the reciprocal of the area of the bottle

7. And now for something completely different

8. See if you can estimate the shape of the bottle

9. Here’s the data collected from the bottle mL of H2O AddedTotal VolumeHeight of Water Column (cm) 000.00 30 0.40 30600.85 30901.35 301201.95 301502.68 301803.55 302104.80 302407.80 302708.984981645 303009.91538457 3033010.65970691 3036011.47846148 3039012.44608053 1040015 1041016 1042017 542519 543021

10. Task 2: See if you can eyeball the shape of the bottle

11. Task 3: Graph the bottle Given the data and the formula for area come up with a way to calculate the radius for each data point. See if any unit conversions are needed Come up with a graph of the Bottle’s Radius vs. Height

12. Given To Us Some Collected Data We can assume that the bottle has a circular circumference. Area circle =  r 2 Volume = Area circle *height

13. The Data mL of H2O AddedTotal VolumeHeight of Water Column (cm) 000.00 30 0.40 30600.85 30901.35 301201.95 301502.68 301803.55 302104.80 302407.80 302708.984981645 303009.91538457 3033010.65970691 3036011.47846148 3039012.44608053 1040015 1041016 1042017 542519 543021

14. height radius area Volume

15. Here’s What I Did

16. Which volume to use? Volume Added Total Added

17. Which height to use? Volume Added Total Added

18. Which height to use? Volume Added Total Added

19. Just how do you get h? height

20. Check unit conversions

21. Here’s What I Did Height difference was calculated by subtracting the current liquid height from the previous one. Height Difference (cm)Width of Glass 4.887264093 0.44.887264093 0.454.607756776 0.54.371301895 0.63.990434422 0.733.617715189 0.873.313875414 1.252.764654066 31.784576526 1.1849816452.839487699 0.9304029253.204499955 0.744322343.582739866 0.8187545743.41600843 0.9676190423.142270731 2.5539194741.116687298 11.784576526 1 20.892288263 2

22. Here’s What I Did mL of H2O AddedTotal Volume Height of Water Column (cm) Height Difference (cm)Width of Bottle 000.004.887264093 30 0.400.44.887264093 30600.850.454.607756776 30901.350.54.371301895 301201.950.63.990434422 301502.680.733.617715189 301803.550.873.313875414 302104.801.252.764654066 302407.8031.784576526 302708.9849816451.1849816452.839487699 303009.915384570.9304029253.204499955 3033010.659706910.744322343.582739866 3036011.478461480.8187545743.41600843 3039012.446080530.9676190423.142270731 10400152.5539194741.116687298 104101611.784576526 104201711.784576526 54251920.892288263 54302120.892288263