Geometry - Areas and Volumes

Ms. Orr, May 11, 2020

Geometry - Areas and Volumes

Table of Contents

  1. Area
  2. Surface Area
    1. Net of Hexagonal Prism
    2. Unwrapping a Cylinder: REVAMPED!
    3. Square Pyramid: Underlying Anatomy
    4. Curved Surface Area of Cones
    5. Surface Area: Intuitive Introduction
    6. Nets of the Cube (11 Different Nets!)
    7. Cone Anatomy
  3. Volumes
    1. Build Your Own Right Triangular Prism (V2)!
    2. Volume of Cylinder vs. Cone (Part 1)
    3. Volume of Cylinder vs. Cone (Part 2)
    4. Volume of Pyramids as it compares to the volume of Prisms
  4. Slicing 3-D Shapes
    1. Sections of Cones
    2. Sections of Triangular Pyramids
    3. Sections of Rectangular Pyramids

1.

Area


    This chapter does not contain any resources yet.

2.

Surface Area

  • 1. Net of Hexagonal Prism
  • 2. Unwrapping a Cylinder: REVAMPED!
  • 3. Square Pyramid: Underlying Anatomy
  • 4. Curved Surface Area of Cones
  • 5. Surface Area: Intuitive Introduction
  • 6. Nets of the Cube (11 Different Nets!)
  • 7. Cone Anatomy

2.1.

Net of Hexagonal Prism

– Ms. Orr

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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3.

Volumes

  • 1. Build Your Own Right Triangular Prism (V2)!
  • 2. Volume of Cylinder vs. Cone (Part 1)
  • 3. Volume of Cylinder vs. Cone (Part 2)
  • 4. Volume of Pyramids as it compares to the volume of Prisms

3.1.

Build Your Own Right Triangular Prism (V2)!

The applet below lets you build a right triangular prism with the specifications listed. [br][br][i][color=#0000ff][b]Explore![/b][/color][/i][br][br]You can also use this resource to assess results of any problems you complete that for which you need to find a triangular prism's lateral area (LA), total surface area (TSA), and/or volume (V). [br][br][b][color=#1e84cc]To explore this resource in Augmented Reality, see the directions below this applet. [/color][/b][br]
TO EXPLORE IN AUGMENTED REALITY:
1) Open up GeoGebra's 3D app on your device. [br][br]2) Press on the 3 horizontal bars (upper left). Select OPEN. [br][br]3) [b]To virtually explore a triangular prism, [/b]type[b] j6xVky5C[/b] [br] in the search bar. (Code = case sensitive). Select what appears. [br][br]IMPORTANT! [br][br]4) Use the [b]prismheight, triangleheight, and oneside[/b] sliders to alter the prism height, triangle height, and [br] purple side (respectively). [br][br] The [b]b[/b] slider controls the horizontal side (edge) of the triangle. Note b = 6 to start. [br][br] [b]TO CREATE A TRIANGLE THAT HAS BLUE ANGLE OBTUSE, find the line that says "v = false". [br][/b] Then edit this line so it says [b]v = true[/b]. [br] To go back to having this blue angle be right or acute, simply make this line [b]v = true. [br][br][/b] [b]To show the TSA, LA, and V[/b] values, simply make the values of [b]m_2, n_2, & o_2 true[/b], respectively. [br]
– Ms. Orr, Tim Brzezinski

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4.

Slicing 3-D Shapes

  • 1. Sections of Cones
  • 2. Sections of Triangular Pyramids
  • 3. Sections of Rectangular Pyramids

4.1.

Sections of Cones

Drag the blue points to see the different sections of the cone.
Anthony Or. GeoGebra Institute of Hong Kong
– Anthony OR 柯志明

4.2.

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4.3.

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Information