GEOMETRY

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GEOMETRY
The Wonderful World of Pi
Grade 7
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Math in our World
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Math in our World

• Who uses Math?

• What do we use it for?

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Types of Math

• Arithmetic
• Algebra
• Geometry
• Trigonometry
• Calculus

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Geometry

• Shapes
• -Squares

• -Triangles

-Rectangles
-Circles
-Ovals
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Definitions

• Perimeter Distance around a shape.
• Area Space within a shape.
• Volume Space within a 3D object.

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Definitions

• Circumference Distance around the circle.
• Diameter Distance across the middle of the
  circle.
• Radius Distance from the center to the side of
  the circle.

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Symbols In Geometry
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Symbols In Geometry
Pi
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Definition of Pi

• Pi is equal to the circumference divided by the
  diameter or
• 2 x radius.
• piC/2r

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FAQS About Pi

• Who discovered pi?
• How long is pi?
• Why is pi important?
• Is it true for all circles?

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Who discovered pi?

• Ancient Babylonians Found the area of a
  circle by 3(r2).
• Ancient Egyptians Found the area by
• (8d)/92.
• Archimedes of Syracuse First theoretical
  calculation of value pi.

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How long is pi?

• Pi is generally written 3.14159
• Pi is a never ending number.

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How long is pi?

• 3. 14159 26535 89793 23846 26433 83279 50288
  41971 69399 37510 58209 74944 59230 78164 06286
  20899 86280 34825 34211 70679 82148 08651 32823
  06647 09384 46095 50582 23172 53594 08128 48111
  74502 84102 70193 85211 05559 64462 29489 54930
  38196 44288 10975 66593 34461 28475 64823 37867
  83165 27120 19091 45648 56692 34603 48610 45432
  66482 13393 60726 02491 41273 72458 70066 06315
  58817 48815 20920 96282 92540 91715 36436 78925
  90360 01133 05305 48820 46652 13841 46951 94151
  16094 33057 27036 57595 91953 09218 61173 81932
  61179 31051 18548 07446 23799 62749 56735 18857
  52724 89122 79381 83011 94912 98336 73362 44065
  66430 86021 39494 63952 24737 19070 21798 60943
  70277 05392 17176 29317 67523 84674 81846 76694
  05132 00056 81271 45263 56082 77857 71342 75778
  96091 73637 17872 14684 40901 22495 34301 46549
  58537 10507 92279 68925 89235 42019 95611 21290
  21960 86403 44181 59813 62977 47713 09960 51870
  72113 49999 99837 29780 49951 05973 17328 16096
  31859 50244 59455 34690 83026 42522 30825 33446
  85035 26193 11881 71010 00313 78387 52886 58753
  32083 81420 61717 76691 47303 59825 34904 28755
  46873 11595 62863 88235 37875 93751 95778 18577
  80532 17122 68066 13001 92787 66111 95909 21642
  01989 ...

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Why is pi important?

• To find the area of a circle.
• To find the perimeter of a circle.
• To find the volume of an object

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Is it true for all circles?
62.83
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Pi C/2r
62.83/(210)
3.1415
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Is it true for all circles?
37.7
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Pi C/2r
37.7/(26)
3.1416
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Is it true for all circles?
18.85
3
Pi C/2r
18.85/(23)
3.1416
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Is it true for all circles?

• 3 values 3.1415, 3.1416, 3.1416
• WHY?

Rounding error in measurement
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• p
• is a
• Constant !

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What are some uses of Pi?

• Perimeter of circle.

• Area of circle.

• Volume of cylinders, cones, and other round
  objects.

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Perimeter of a Circle

• Perimeter of circle
• circumference of circle
• C 2pr

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Perimeter of a Circle
2
Circumference 2pr
Answer 12.5663
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Area of Circle

• Area is measured using square units.

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Area 1 unit2
1
1
1
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Area of Circle
1
Area pr2
Answer 3.1416 unit2
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Volume of Cylinder
1
5
Volume area height pr2 h
Answer 15.7079
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Key Points

• Pi p
• Pi 3.1415
• Pi is a CONSTANT.
• Pi is a never-ending number.

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Key Points

• Perimeter Circumference
• C 2pr
• C pd
• Area pr2
• Volume area height
• pr2 h

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Find the area of the following circle

• A. 78.5398 cm2
• B. 49.3480 cm2
• C. 15.7079 cm2
• D. 246.7401 cm2

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Incorrect

• Sorry, try again

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Review

• Remember, area is the space within the object.
• A pr2

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Correct!
You've gotten it!
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Find the Perimeter

• A. 62.832 m2
• B. 31.416 m
• C. 62.832 m
• D. 98.696 m

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Incorrect

• Sorry, try again

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Review

• Remember, perimeter circumference
• C 2pr

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Correct!
Excellent Job!