Geometric Measurement and Dimension (GMD) Cluster

Tim Brzezinski, JohnCMorris, Nov 14, 2017

MAFS.912.G-GMD.1.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieris principle, and informal limit arguments. MAFS.912.G-GMD.1.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. MAFS.912.G-GMD.2.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Table of Contents

  1. MAFS.912.G-GMD.1.1
    1. TRUE MEANING of π
    2. Circumference = ? (Animation)
    3. Animation 66
    4. Circumference = ? (Animation II)
    5. Animation 70
    6. Animation 65
    7. Parallelogram: Area
    8. Animation 202
    9. Triangle Area Action! (V1)
    10. Triangle Area Action!!! (V2)
    11. Animation 175
    12. Circle Area (by Peeling)
    13. Circle Area (By Peeling!)
    14. Area of a Circle - without words (Animation 38)
    15. Area of a Circle (III)
    16. Area of a Circle (by Peeling)
    17. Area of a Circle II
    18. Volume of a Rectangular Prism
    19. Figure 6.7 Cavalieri's principle
    20. Cavalieri's Principle
    21. Mailbox? Backpack? (Composite Solid)
    22. Washer Action!!! (1)
    23. Animation 169
    24. Trisecting the Cube into 3 Pyramids
    25. Volume of Pyramids
    26. Volume of Pyramids - Chinese Proof
    27. SolveMyMaths Action 3A!
    28. SolveMyMaths Action 3B!
    29. Animation 203
    30. SolveMyMaths Action 4!
    31. Animation 204
    32. 4 Triangles Action!!!
    33. Animation 179
  2. MAFS.912.G-GMD.1.3
    1. Unwrapping a Cylinder
    2. Unwrapping a Cylinder: REVAMPED!
    3. Volume of Spheres
    4. Volume of Spheres with Proof
    5. A sphere in a cylinder.
    6. Surface Area of Spheres
    7. Volumes and Surface Areas of Similar Cuboids
    8. Square Pyramid: Underlying Anatomy
    9. oblique and right pyramid - Cavalieri
    10. Right Triangular Prism!
    11. Adjustable Triangular Prism
    12. Sphere Peeling: Volume
    13. Net of a Cone
    14. Curved Surface Area of Cones (Combined Version)
  3. MAFS.912.G-GMD.2.4
    1. Sections of Rectangular Prisms (Cuboids)
    2. Sections of Triangular Prisms
    3. Sections of Cylinders
    4. Sections of Rectangular Pyramids
    5. Sections of Triangular Pyramids
    6. Sections of Cones
    7. Sections of Spheres
    8. Exploring Sections of Cubes
    9. 11 Nets of the Cube
    10. Cube Geometry: Shortest Path Between Points - A Net
    11. Cube Dissection Problem
    12. Rotating a Triangle Around a Coordinate Axis
    13. Box with Open Top
    14. Cross Section? (1)

1.

MAFS.912.G-GMD.1.1

  • 1. TRUE MEANING of π
  • 2. Circumference = ? (Animation)
  • 3. Animation 66
  • 4. Circumference = ? (Animation II)
  • 5. Animation 70
  • 6. Animation 65
  • 7. Parallelogram: Area
  • 8. Animation 202
  • 9. Triangle Area Action! (V1)
  • 10. Triangle Area Action!!! (V2)
  • 11. Animation 175
  • 12. Circle Area (by Peeling)
  • 13. Circle Area (By Peeling!)
  • 14. Area of a Circle - without words (Animation 38)
  • 15. Area of a Circle (III)
  • 16. Area of a Circle (by Peeling)
  • 17. Area of a Circle II
  • 18. Volume of a Rectangular Prism
  • 19. Figure 6.7 Cavalieri's principle
  • 20. Cavalieri's Principle
  • 21. Mailbox? Backpack? (Composite Solid)
  • 22. Washer Action!!! (1)
  • 23. Animation 169
  • 24. Trisecting the Cube into 3 Pyramids
  • 25. Volume of Pyramids
  • 26. Volume of Pyramids - Chinese Proof
  • 27. SolveMyMaths Action 3A!
  • 28. SolveMyMaths Action 3B!
  • 29. Animation 203
  • 30. SolveMyMaths Action 4!
  • 31. Animation 204
  • 32. 4 Triangles Action!!!
  • 33. Animation 179

1.1.

TRUE MEANING of π

Note: LARGE WHITE POINT is MOVEABLE.
1.
How many diameters were we able to wrap perfectly around this circle? [br](Round your answer to the nearest 0.01.)
2.
Move the LARGE WHITE POINT a bit (to change the size of the circle). Does your answer to question (1) change at all?
3.
Does your response for (1) look familiar? Where you have you seen this number before?
Quick (Silent) Demo
– Tim Brzezinski

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2.

MAFS.912.G-GMD.1.3

  • 1. Unwrapping a Cylinder
  • 2. Unwrapping a Cylinder: REVAMPED!
  • 3. Volume of Spheres
  • 4. Volume of Spheres with Proof
  • 5. A sphere in a cylinder.
  • 6. Surface Area of Spheres
  • 7. Volumes and Surface Areas of Similar Cuboids
  • 8. Square Pyramid: Underlying Anatomy
  • 9. oblique and right pyramid - Cavalieri
  • 10. Right Triangular Prism!
  • 11. Adjustable Triangular Prism
  • 12. Sphere Peeling: Volume
  • 13. Net of a Cone
  • 14. Curved Surface Area of Cones (Combined Version)

2.1.

Unwrapping a Cylinder

– Tim Brzezinski

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3.

MAFS.912.G-GMD.2.4

  • 1. Sections of Rectangular Prisms (Cuboids)
  • 2. Sections of Triangular Prisms
  • 3. Sections of Cylinders
  • 4. Sections of Rectangular Pyramids
  • 5. Sections of Triangular Pyramids
  • 6. Sections of Cones
  • 7. Sections of Spheres
  • 8. Exploring Sections of Cubes
  • 9. 11 Nets of the Cube
  • 10. Cube Geometry: Shortest Path Between Points - A Net
  • 11. Cube Dissection Problem
  • 12. Rotating a Triangle Around a Coordinate Axis
  • 13. Box with Open Top
  • 14. Cross Section? (1)

3.1.

Sections of Rectangular Prisms (Cuboids)

Drag the blue points to see the different sections of the rectangular prism (cuboid).
Anthony Or. GeoGebra Institute of Hong Kong
– Anthony OR 柯志明

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