Körper

Michael Porics, Aug 9, 2017

Table of Contents

  1. Quader
    1. Rectangular Prism: Anatomy Exploration
    2. Quadernetze
    3. Volumen eines Quaders
    4. Volume: Intuitive Introduction
    5. Cross sections of a cube
    6. Cross Sections of a Cube
    7. Surface Area: Introductory Exercises
    8. Volumes of Cuboids
    9. Orthographic Views of a Solid
  2. Prisma
    1. Triangular Prism: Anatomy Exploration
    2. Adjustable Triangular Prism
    3. Build Your Own Right Triangular Prism!
    4. Diagonal Hint for a Rectangular Prism
    5. Prism Nets
    6. GeoGebra 3D: Getting Started - Part 4
    7. Schwimmbad
    8. 3D Modeling Using Coordinates (1): Building Rectangular Prisms
    9. 3D Modeling Using Coordinates (2): Building Composite Solids
  3. Kugel
    1. Modifiable Torus
    2. Sphere + Plane = ?
    3. Sections of a Sphere
    4. Ellipsoid: Quick Exploration Template
    5. Das Volumen einer Kugel
    6. Kugelsegment, Kugelkalotte
    7. Kugelvolumen .02
  4. Drehzylinder-und Kegel
    1. Zylindernetz
    2. Unwrapping a Cylinder: REVAMPED!
    3. Net of a Cone
    4. Kegelmantel
    5. Cone Anatomy
    6. Zylinder mit Loch
    7. Prisma und Zylinder
  5. Pyramide
    1. Square Pyramid: Underlying Anatomy
    2. Regelmäßige Pyramiden .02
  6. Zusammengesetzte Körper
    1. Pyramid on Rectangular Prism
    2. Silo
    3. Mailbox? Backpack? (Composite Solid)
    4. Washer Action!!! (1)
    5. Rotating Plane Figure Around an Axis
    6. Körper mit gleichem Grundriss
    7. Composite Solid 1

1.

Quader

  • 1. Rectangular Prism: Anatomy Exploration
  • 2. Quadernetze
  • 3. Volumen eines Quaders
  • 4. Volume: Intuitive Introduction
  • 5. Cross sections of a cube
  • 6. Cross Sections of a Cube
  • 7. Surface Area: Introductory Exercises
  • 8. Volumes of Cuboids
  • 9. Orthographic Views of a Solid

1.1.

Rectangular Prism: Anatomy Exploration

BIG POINT is moveable.
– Tim Brzezinski

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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2.

Prisma

  • 1. Triangular Prism: Anatomy Exploration
  • 2. Adjustable Triangular Prism
  • 3. Build Your Own Right Triangular Prism!
  • 4. Diagonal Hint for a Rectangular Prism
  • 5. Prism Nets
  • 6. GeoGebra 3D: Getting Started - Part 4
  • 7. Schwimmbad
  • 8. 3D Modeling Using Coordinates (1): Building Rectangular Prisms
  • 9. 3D Modeling Using Coordinates (2): Building Composite Solids

2.1.

Triangular Prism: Anatomy Exploration

LARGE POINTS are moveable.
Quick Silent Demo
– Tim Brzezinski

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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2.7.

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2.8.

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2.9.

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3.

Kugel

  • 1. Modifiable Torus
  • 2. Sphere + Plane = ?
  • 3. Sections of a Sphere
  • 4. Ellipsoid: Quick Exploration Template
  • 5. Das Volumen einer Kugel
  • 6. Kugelsegment, Kugelkalotte
  • 7. Kugelvolumen .02

3.1.

Modifiable Torus

TO EXPLORE IN AUGMENTED REALITY:
1) Open up GeoGebra 3D app on your device. [br][br]2) Go to the MENU (horizontal bars) in the upper left corner. Select OPEN. [br] In the Search GeoGebra Resources input box, type [b]h2fkfsfm[/b][br] (Note this is the resource ID = last 8 digits of the URL for this resource.)[br][br]How do the values of[b] R [/b]and [b]r[/b] affect the graph of this [b][color=#1e84cc]surface[/color][/b]? [br][br][b]What happens when R = 0? [br][br]What happens when R = r? [br][br]What happens when R > r? [br][br]What happens when R < r ? [/b]
– Tim Brzezinski

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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4.

Drehzylinder-und Kegel

  • 1. Zylindernetz
  • 2. Unwrapping a Cylinder: REVAMPED!
  • 3. Net of a Cone
  • 4. Kegelmantel
  • 5. Cone Anatomy
  • 6. Zylinder mit Loch
  • 7. Prisma und Zylinder

4.1.

Zylindernetz

Zylindernetz
Wolfgang Wengler
– Wolfgang Wengler

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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5.

Pyramide

  • 1. Square Pyramid: Underlying Anatomy
  • 2. Regelmäßige Pyramiden .02

5.1.

Square Pyramid: Underlying Anatomy

Interact with this [b][color=#38761d]square pyramid[/color][/b] for a minute or two. [br][br]You can alter the base and height of this [color=#38761d][b]square pyramid[/b][/color] by dragging the 2 white points. [br][br]How would you describe the relationship between a square pyramid's [b]LATERAL HEIGHT[/b] and its [b]TRUE HEIGHT? [br][br][color=#1e84cc]To explore this resource in Augmented Reality, see the directions below the applet. [/color][/b]
Suppose each edge of the square base measures 10 cm. If this square pyramid's lateral height measures 13 cm, what would its true height be? [br][br]What would the pyramid's [b]lateral area[/b] be? What would its [b]total surface area[/b] be? [br][br]What would its [b]volume[/b] be?
TO EXPLORE IN AUGMENTED REALITY:
1) Open GeoGebra 3D app on your device. [br][br]2) Press the 3 horizontal bars (upper left corner). Select OPEN. [br][br]3) In the SEARCH TAB that appears, type [b]V9cAn76T[/b][br] Note this string of characters can be found in the URL here. [br] Be sure to either copy & paste this code or type it just the way you see it here. [br][br]4) The slider named [b]n [/b]does the entire animation. Slide this completely to the right. [br] When in 3D view, you can move the white point (outside the pyramid) up or down to change its height. [br] You can also drag the large white points on the pyramid's base to adjust the base size.
– Tim Brzezinski

5.2.

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6.

Zusammengesetzte Körper

  • 1. Pyramid on Rectangular Prism
  • 2. Silo
  • 3. Mailbox? Backpack? (Composite Solid)
  • 4. Washer Action!!! (1)
  • 5. Rotating Plane Figure Around an Axis
  • 6. Körper mit gleichem Grundriss
  • 7. Composite Solid 1

6.1.

Pyramid on Rectangular Prism

BIG POINTS are moveable
– Tim Brzezinski

6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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6.7.

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Information