Optimization.notebook
December 16, 2014
Optimization
Learning Goals:
• determine the properties of shapes that will give maximum area with minimum perimeter
• determine the properties of shapes that will give maximum volume with minimum area
Dec 16­7:55 AM
Minimum perimeter
Maximum area
­a square (a square is a special type of rectangle)
Max volume of a prism
­a square (a square is a special type of rectangle)
Minimum surface area of a prism
­a cube (a cube is a special rectangular prism)
­a cube (a cube is a special rectangular prism)
Minimum surface area of a cylinder
Max volume of a cylinder
­diameter and height will be equaldiameter = 2r height = 2r
diameter and height will be equaldiameter = 2r height = 2r
Dec 16­7:56 AM
Area
Perimeter
Optimization
Volume
Surface Area
Jun 2­7:39 AM
Minimizing Perimeter
I have an area of 64 m2 and I want to build a fence around it that had the smallest (minimum) perimeter so I can save money on buying fencing. What would that minimum perimeter be?
Jun 1­8:34 PM
Dec 16­8:12 AM
Example: A building supply store donates 100 m of fencing to a daycare. The fencing will be used to create a rectangular play area. Which dimensions will give the largest possible area? What is the area?
Dec 16­8:12 AM
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Optimization.notebook
Example: Tony wants to fence 50 m2 of his backyard to make a rectangle vegetable garden. Determine the dimensions of the garden with the least perimeter. What is the smallest perimeter possible?
Dec 16­8:13 AM
December 16, 2014
Surface Area and Volume
Why would you want to optimize surface area and volume? Who would use these calculations?
Dec 16­8:23 AM
Example: Determine the dimensions of the cylinder with maximum volume that can be made with 600 cm2 of aluminum. Round the dimensions to the nearest hundredth of a centimeter. What is the volume of this cylinder?
Example: Rosa constructs a rectangular prism using exactly 384 cm2 of cardboard. It has the greatest volume possible. What are the dimensions of the prism? What is the volume?
Dec 16­8:23 AM
Maximizing Area
Jun 1­8:30 PM
Dec 16­8:24 AM
Minimizing Perimeter
Jun 1­8:36 PM
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Optimization.notebook
Minimizing Surface Area and Maximizing Volume of a Square Based Pyramid
December 16, 2014
Looking at our rectangular cubes ­ how do you think you can optimize surface area and volume?
Why would you want to optimize surface area and volume?
Minimizing surface area for a given volume is important when designing packages and containers to save on materials and reduce head loss. The same goes for maximizing volume for a given surface area.
Jun 1­8:37 PM
Jun 1­8:39 PM
Homework
Page 441 #1­4, 6,9
Page 487 # 1
Page 495 #1­3
Page 501­502 #1­3
Jun 1­8:39 PM
Jun 1­8:40 PM
Jun 2­7:40 AM
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