Orchard 15 ­ Block 15 ­ Polygoning the Circle_pi.notebook
October 03, 2012
Bell Work
• Choose your own seat BUT you must sit with at least 2 people who were not at your table last time
• Collate pg.229 WS
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Orchard 15 ­ Block 15 ­ Polygoning the Circle_pi.notebook
October 03, 2012
Bell Work
• At your tables…
Share your formulas in #2 with one another and try to simplify them to the form
Circumference = kcr
Area = kar2
• Then complete “Octagoning the Circle”
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Orchard 15 ­ Block 15 ­ Polygoning the Circle_pi.notebook
October 03, 2012
Constant of Proportionality
• The circumference of the circle is proportional to its radius.
• The area of the circle is proportional to the square of its radius.
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Orchard 15 ­ Block 15 ­ Polygoning the Circle_pi.notebook
October 03, 2012
Octagoning the Circle ­ Perimeter
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Orchard 15 ­ Block 15 ­ Polygoning the Circle_pi.notebook
October 03, 2012
Octagoning the Circle ­ Perimeter
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Orchard 15 ­ Block 15 ­ Polygoning the Circle_pi.notebook
October 03, 2012
Octagoning the Circle ­ Area
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Orchard 15 ­ Block 15 ­ Polygoning the Circle_pi.notebook
October 03, 2012
Octagoning the Circle ­ Area
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Orchard 15 ­ Block 15 ­ Polygoning the Circle_pi.notebook
October 03, 2012
Constants of Proportionality…
Shape Perimeter
Area
Circle
kcr =
kar2 =
Square
8r
4r2
Hexagon
6.93r
3.46r2
Octagon
6.63r
3.31r2
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Orchard 15 ­ Block 15 ­ Polygoning the Circle_pi.notebook
October 03, 2012
Polygoning the Circle
• Organize your work on the worksheet:
• Clubs = Pentagon (5 sides)
• Diamonds = Septagon (7 sides)
• Hearts = Nonagon (9 sides)
• Spades = Decagon (10 sides)
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Orchard 15 ­ Block 15 ­ Polygoning the Circle_pi.notebook
October 03, 2012
Polygoning Worksheet
• Clubs = 30 sides, and 360 sides
• Diamonds = 25 sides, and 300 sides
• Hearts = 20 sides, and 200 sides
• Spades = 15 sides, and 100 sides
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Orchard 15 ­ Block 15 ­ Polygoning the Circle_pi.notebook
Shape Circle
Perimeter
October 03, 2012
Area
kcr =
kar2 =
8r
4r2
Pentagon
7.27r
3.63r2
Hexagon
6.93r
3.46r2
Septagon
6.74r
3.37r2
Octagon
6.63r
3.31r2
Nonagon
6.55r
3.28r2
Decagon
6.50r
3.25r2
Square
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12
15
20
25
30
100
200
300
360
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