2. Why the Titanic Sank The Titanic was a British ship that set sail on April 10, 1912. It made two stops before heading toward New York. It never made it there. It sank on April 15 after hitting an ice berg.

3. What happened to the Titanic? Click on this video to see the sequence of events that led to the sinking of the Titanic. http://youtu.be/qCv1jKHfFiY

4. Where is the Titanic now? Click on this video to see footage of the wreck of the Titanic. http://youtu.be/6Z7REEnwKOQ

5. Why the Titanic Sank To get a sense of how massive the Titanic was, this illustration gives an idea of the scale of the ship.

6. Why the Titanic Sank The key to sailing a ship of this size is to make sure the density of the ship is such that it will float on water. Density is defined as the ratio of mass to volume.

7. Why the Titanic Sank The density of water is defined as 1. So in order for the Titanic to float, it needed a density less than 1.

8. Why the Titanic Sank To simplify the calculation of density, let’s assume that the bulk of the ship is in the shape of a triangular prism, as shown here.

9. Why the Titanic Sank The net on the left shows the three dimensions used to calculate the volume of a triangular prism.

10. Why the Titanic Sank The length, width, and height measurements are those of the Titanic. The mass of the ship was 46,000 tons.

11. Why the Titanic Sank The measurements provided yield a density of 0.41 for the Titanic, well below the density needed to float. This also means that the Titanic could still take on water before sinking.

12. Why the Titanic Sank Once the Titanic started taking on water, its mass would increase while its volume decreased. This is shown in the expression above. Losing volume and gaining mass is a deadly combination that will lead to a ship sinking.

13. Why the Titanic Sank We can graph the function representing the changing density to see where it intersects the graph y = 1. This is the point where the ship has taken on too much water, making its density greater than 1.

14. Why the Titanic Sank Once the ship gained about 40% more mass in water, then the ship had too much density to float. One of the features that was intended to prevent too much water was the set of 16 water-tight sections of the ship.

15. Why the Titanic Sank However, when the Titanic struck the ice berg, five (possibly six) compartments were damaged. This would have allowed enough water to sink the Titanic.

16. Or would it? Click on this video to see what additional problems emerged with these water-tight compartments. http://youtu.be/xZ8Olj0xs4Q

17. Why the Titanic Sank Do you think if the 16 compartments had been fully water tight that the Titanic might have stayed afloat long enough for the passengers to be rescued?

18. This presentation was adapted from our Geometry Applications video series, “Area and Volume.” Click here for more information. http://www.media4math.com/Geo metry_Applications.asp