Chapter 9 Review Notes


3 words about Chapter 9   -   Optimizing, Minimizing, Maximizing

3 shapes in Chapter 9  -    Rectangle, Squared-based Prism, Cylinder

 

9.1 - Max Area given Perimeter

 

Rectangles: same perimeter does not equal same area

Find max area with given perimeter

 

Ex.

 

Perimeter = 100

100/4 = 25

25² = 625cm²

 

 

 

9.2 - Optimizing Perimeter of a Rectangle

 

Optimal shape with:

- 4 sides = square

- 3 sides = P/4 + P/4+P/2

 

Ex. 300 m of fence

 

- 4 sides – 300/4 = 75 m per side

 

- 3 sides – 300/4 = 75 m x 2 short sides

150 x 1 long side

 

9.3 - min Surface area Given the Volume (Square Based Prism)

 

- Square Based Prism

- Find min SA for given volume

- Use formula V=s³ to find length of side

 

 

9.4 - Max Volume Given Surface Area (Square Based Prism)

 

- Find max volume given the Surface Area

- Use formula SA = 6s²

- Cube is the ideal figure for optimization

 

9.5 - Max Volume Given Surface Area (Cylinder)

 

- Cylinder

- Find max volume given SA

- SA = 6Π² h=2r

 

9.6 - Max Surface Area given Volume (Cylinder)

 

- Cylinder

- Find min. SA for given volume

- V=2Π³ h=2r