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# NCTM 2012 Presentation 3

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This is the third of the presentations we gave at the TI booth at NCTM 2012 in Philly.

This is the third of the presentations we gave at the TI booth at NCTM 2012 in Philly.

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### Transcript

• 1. Algebra & Geometry Resources for the TN-Nspire Media4Math includes a variety of free and premium resources, including short video tutorials on the Nspire, Math in the News, and other tutorials.
• 2. Algebra & Geometry Resources for the TN-Nspire DVD Library, Algebra Applications.
• 3. Algebra & Geometry Resources for the TN-Nspire DVD Library, Geometry Applications.
• 4. Algebra & Geometry Resources for the TN-Nspire This presentation on the Titanic comes from the Geometry Applications: Area and Volume and includes algebra and geometry connections.
• 5. Algebra & Geometry Resources for the TN-Nspire This illustration gives a sense of the size and scale of the Titanic.
• 6. Algebra & Geometry Resources for the TN-Nspire To better understand how a ship of this size can float, we explore the concept of density.
• 7. Algebra & Geometry Resources for the TN-Nspire By definition the density of water is 1 (in units of gm/cm3). A density less than 1 causes an object to float; greater than 1 and the object sinks.
• 8. Algebra & Geometry Resources for the TN-Nspire As a simple example, look at a cube of length s and mass M. Its density is M/s3.
• 9. Algebra & Geometry Resources for the TN-Nspire This is a rational function. Given different values of M, the cube will float based on where its graph is relative to y = 1, the red line.
• 10. Algebra & Geometry Resources for the TN-Nspire We can estimate the volume of the Titanic by looking at the shape of the hull and main body of the ship.
• 11. Algebra & Geometry Resources for the TN-Nspire A triangular prism provides a reasonable estimate of this folume.
• 12. Algebra & Geometry Resources for the TN-Nspire This is the net for a triangular prism.
• 13. Algebra & Geometry Resources for the TN-Nspire Given the dimensions shown, the volume of the triangular prism is found using this formula.
• 14. Algebra & Geometry Resources for the TN-Nspire These are the dimensions for the Titanic. The linear dimensions are for the “rectancular prism” section and the displacement is the mass of the ship.
• 15. Algebra & Geometry Resources for the TN-Nspire On the Nspire, create a Calculator Window and assign the values for mass to a variable called “mass.”
• 16. Algebra & Geometry Resources for the TN-Nspire Make sure the units for mass are are gm. You can operate on the “mass” variable and reassign the result to the same variable.
• 17. Algebra & Geometry Resources for the TN-Nspire Create a “volume” variable and calculate the volume of the triangular prism. Then calculate the density.
• 18. Algebra & Geometry Resources for the TN-Nspire The estimated density of the Titanic is less than 1 (and probably a bit higher due to the triangular prism volume).
• 19. Algebra & Geometry Resources for the TN-Nspire When the Titanic struck the iceberg a number of punctures caused water to flow into the hull.
• 20. Algebra & Geometry Resources for the TN-Nspire When a ship takes on water, the loss in volume is immediately converted to mass. This leads to a quick increase in density.
• 21. Algebra & Geometry Resources for the TN-Nspire This density expression shows that as the volume decreases, the mass increases. The variable x is the percent of volume lost.
• 22. Algebra & Geometry Resources for the TN-Nspire This graph shows that when about 58% of the hull is filled with water, it will sink. But this overestimates the volume of the hull.
• 23. Algebra & Geometry Resources for the TN-Nspire This graph scales the volume down and gets us to a more accurate estimate of when the ship will sink.
• 24. Algebra & Geometry Resources for the TN-Nspire The Titanic had 16 watertight compartments. When it struck the iceberg, 5 (possibly 6) of them were punctured.