math in the news: 5/15/11
TRANSCRIPT
5/16/11
Flooding
3D Geometry
• Memphis is located right by a bend in the Mississippi River.
• This satellite photo from Google Maps shows the Mississippi prior to the floods.
Flooding
3D Geometry
• This image shows the extensive flooding that has occurred.
• Given the two images, how can we estimate the amount of water that makes up this flood?
Flooding
3D Geometry
• In this illustration we see the portion of the Mississippi River that flows past Memphis.
Flooding
3D Geometry
• Think of this portion of the river as a curved rectangular prism, as shown.
Flooding
3D Geometry
• If we “straighten out” this rectangular prism, we get a standard-looking rectangular prism.
• The volume of a rectangular prism is length • width • height
Flooding
3D Geometry
• But this volume only provides the amount of water when the river isn’t flooding.
• What we’re interested in is a second rectangular prism that makes up the excess water.
Flooding
3D Geometry
• We can use this diagram to find the volume of flooding for different amounts of water.
• The Volume is a linear function for different values of x, the height of the flooding, in inches.
Flooding
3D Geometry
• In this graph, the x-values are the inches of flooding occurring, and the y-values are volume of flood water.
Flooding
3D Geometry
• But remember that the river is also flowing at an average speed of 2 mph.
• This means that every hour another rectangular prism’s worth of water flows through, increasing the amount of flooding.
Flooding
A Family of Linear Functions
• Because a can vary, we get a family of linear functions. In each case the y-value represents the accumulated volume of flooding for the specific number of days. 2335680000000.
Flooding
3D Geometry
• To see how massive the flooding can be. Take V = 24•f1(2)x and evaluate it for x = 20.
• This would be a situation where 2 inches of flooding occurs for 20 days.
Equivalent to the water from 10 New
Orleans Super Domes!