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Exploring Bottle Dimensions through Graphs and Estimations

Dive into the world of bottle dimensions by graphing total volume vs. height for different circumferences, interpreting slopes, estimating bottle shapes, and calculating radii. Discover the fun of math and science!

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Exploring Bottle Dimensions through Graphs and Estimations

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  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. Check Out The Cool Drawings

  5. What would be the graph for a beaker?

  6. What would be the graph for a flask?

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

  8. And now for something completely different

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

  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 Radius vs. Height

  12. Given To Us • Some Collected Data • We can assume that the bottle has a circular circumference. • Areacircle = r2 • Volume = Areacircle *height

  13. The Data

  14. Volume area radius height

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