Geometric Solids

Renee Fietsam, 10.04.2021

Geometric Solids

Inhaltsverzeichnis

  1. Nets
    1. Net and Surface Area of Triangular Prism
    2. Net of a Square Pyramid
    3. Net of Hexagonal Prism
    4. Nets of the Cube
    5. Net of a Cylinder
    6. Net of a Cone
    7. Net of Icosahedron
    8. Net of Dodecahedron
    9. Nets of Tetrahedron
    10. Rhombicuboctahedron's net
    11. Truncated octahedron's net
  2. Cross Sections
    1. Sections of Rectangular Prisms (Cuboids)
    2. Sections of Cylinders
    3. Sections of Cones
    4. Sections of Spheres
    5. Sections of Triangular Prisms
    6. Sections of Rectangular Pyramids
  3. Solids of Rotation
    1. Rotation of Rectangle
    2. Rotation of Triangle
    3. Rotation of Circle
    4. Solids of revolution - Disk integration - Exploration+Practice
    5. Visualizing Volume of Solids of Revolution about x-axis
  4. Platonic Solids
    1. All solids of Platon rotate
  5. Volume
    1. Volume: Intuitive Introduction
    2. Cavalieri's Principle
    3. Copy of Cavalieri's Principle
    4. Cavalieri's Principle
    5. Trisecting the Cube into 3 Pyramids
    6. Volume of a Sphere via Cavalieri's Principle

1.

Nets

  • 1. Net and Surface Area of Triangular Prism
  • 2. Net of a Square Pyramid
  • 3. Net of Hexagonal Prism
  • 4. Nets of the Cube
  • 5. Net of a Cylinder
  • 6. Net of a Cone
  • 7. Net of Icosahedron
  • 8. Net of Dodecahedron
  • 9. Nets of Tetrahedron
  • 10. Rhombicuboctahedron's net
  • 11. Truncated octahedron's net

1.1.

Net and Surface Area of Triangular Prism

– Tok Hong Da

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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2.

Cross Sections

  • 1. Sections of Rectangular Prisms (Cuboids)
  • 2. Sections of Cylinders
  • 3. Sections of Cones
  • 4. Sections of Spheres
  • 5. Sections of Triangular Prisms
  • 6. Sections of Rectangular Pyramids

2.1.

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 ęŸÆåæ—ę˜Ž

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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3.

Solids of Rotation

  • 1. Rotation of Rectangle
  • 2. Rotation of Triangle
  • 3. Rotation of Circle
  • 4. Solids of revolution - Disk integration - Exploration+Practice
  • 5. Visualizing Volume of Solids of Revolution about x-axis

3.1.

Rotation of Rectangle

– Mr. Lietzow

3.2.

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3.3.

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3.4.

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3.5.

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4.

Platonic Solids

  • 1. All solids of Platon rotate

4.1.

All solids of Platon rotate

– uStas

5.

Volume

  • 1. Volume: Intuitive Introduction
  • 2. Cavalieri's Principle
  • 3. Copy of Cavalieri's Principle
  • 4. Cavalieri's Principle
  • 5. Trisecting the Cube into 3 Pyramids
  • 6. Volume of a Sphere via Cavalieri's Principle

5.1.

Volume: Intuitive Introduction

STUDENTS:
Interact with the applet below for a few minutes. Then answer the questions that follow. [br][br][b][color=#1e84cc]To explore this resource in Augmented Reality, see the directions beneath the questions listed below. [/color][/b]
1.
In the applet above, create a rectangular prism that has its first layer measuring 3 units long by 4 units wide. Suppose this rectangular prism is 2 layers high. How many cubes make up this prism?
2.
In the applet above, create a rectangular prism that has its first layer measuring 5 units long by 3 units wide. How many cubes make up this prism if this prism is 2 layers high? 3 layers high? 10 layers high?
3.
How can we EASILY determine the number of cubes that fit inside ANY rectangular prism? Describe.
TO EXPLORE IN AUGMENTED REALITY:
1) Open up GeoGebra 3D app on your device. [br][br]2) Go to the[b] MENU (horizontal bars)[/b] in the upper left corner. Select [b]OPEN[/b]. [br] In the Search GeoGebra Resources input box, type [b]dp6ghmvv[/b][br] (Note this is the resource ID = last 8 digits of the URL for this resource.)[br][br]3) In the resource that uploads, zoom out and/or adjust the [br] LENGTH, WIDTH, & HEIGHT sliders to create a prism with dimensions you like. [br][br] Press the [b]AR[/b] button in the lower right corner of your 3D screen. Follow the directions that appear.
– Tim Brzezinski

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5.6.

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