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

2. 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.

3. Algebra & Geometry Resources for the TN-Nspire
DVD Library, Algebra Applications.

4. Algebra & Geometry Resources for the TN-Nspire
DVD Library, Geometry Applications.

5. 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.

6. Algebra & Geometry Resources for the TN-Nspire
This illustration gives a sense of the
size and scale of the Titanic.

7. Algebra & Geometry Resources for the TN-Nspire
To better understand how a ship of
this size can float, we explore the
concept of density.

8. 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.

9. 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.

10. 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.

11. 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.

12. Algebra & Geometry Resources for the TN-Nspire
A triangular prism provides a
reasonable estimate of this folume.

13. Algebra & Geometry Resources for the TN-Nspire
This is the net for a triangular prism.

14. Algebra & Geometry Resources for the TN-Nspire
Given the dimensions shown, the
volume of the triangular prism is
found using this formula.

15. 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.

16. 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.”

17. 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.

18. Algebra & Geometry Resources for the TN-Nspire
Create a “volume” variable and
calculate the volume of the triangular
prism. Then calculate the density.

19. 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).

20. Algebra & Geometry Resources for the TN-Nspire
When the Titanic struck the iceberg a
number of punctures caused water to
flow into the hull.

21. 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.

22. 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.

23. 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.

24. 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.

25. 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.