Surface Area & Volume

Tim Brzezinski, Sep 16, 2015

Surface Area & Volume Applets

Table of Contents

  1. Surface Area
    1. Surface Area: Introductory Exercises
    2. Cube: Exploration Template
    3. Nets of the Cube
    4. 11 Nets of the Cube
    5. Net of Hexagonal Prism
    6. Build Your Own Right Triangular Prism (V2)!
    7. Unwrapping a Cylinder
    8. Unwrapping a Cylinder: REVAMPED!
    9. Square Pyramid: Underlying Anatomy
    10. Cone Anatomy
    11. Octahedron: Exploration Template
    12. Tetrahedron: Exploration Template
    13. Dodecahedron: Exploration Template
    14. Icosahedron: Exploration Template
    15. Open Middle (Revamped): Creating Rectangular Prisms with a Given Surface Area
  2. Volume
    1. Box with Open Top
    2. tisect a cube
    3. opening a cube
    4. Volume of Spheres

1.

Surface Area

  • 1. Surface Area: Introductory Exercises
  • 2. Cube: Exploration Template
  • 3. Nets of the Cube
  • 4. 11 Nets of the Cube
  • 5. Net of Hexagonal Prism
  • 6. Build Your Own Right Triangular Prism (V2)!
  • 7. Unwrapping a Cylinder
  • 8. Unwrapping a Cylinder: REVAMPED!
  • 9. Square Pyramid: Underlying Anatomy
  • 10. Cone Anatomy
  • 11. Octahedron: Exploration Template
  • 12. Tetrahedron: Exploration Template
  • 13. Dodecahedron: Exploration Template
  • 14. Icosahedron: Exploration Template
  • 15. Open Middle (Revamped): Creating Rectangular Prisms with a Given Surface Area

1.1.

Surface Area: Introductory Exercises

Take a few minutes to interact with the rectangular prism shown here. After doing so, create one that has a length = 4 units, width = 5 units, and height = 3 units.
How many square units (i.e. "squares") appear on 1 [b][color=#ff00ff]pink face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b][color=#bf9000]gold face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b]white face[/b]?
Use your answers for (1) to determine the TOTAL SURFACE AREA of this rectangular prism. [br]That is, how many square units, or squares, cover the ENTIRE SURFACE of this rectangular prism?
Now create a rectangular prism that has a length = 8 units, width = 3 units, and height = 5 units.
How many square units (i.e. "squares") appear on 1 [b][color=#ff00ff]pink face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b][color=#bf9000]gold face[/color][/b]? [br]How many square units (i.e. "squares") appear on 1 [b]white face[/b]?
Use your answers for (3) to determine the TOTAL SURFACE AREA of this rectangular prism. [br]That is, how many square units, or squares, cover the ENTIRE SURFACE of this rectangular prism?
Overall, how we can determine the total surface area (number of squares) that cover the entire surface of a rectangular prism? Describe.
– Tim Brzezinski

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1.11.

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1.15.

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2.

Volume

  • 1. Box with Open Top
  • 2. tisect a cube
  • 3. opening a cube
  • 4. Volume of Spheres

2.1.

Box with Open Top

Suppose a big square has 4 congruent smaller squares (each having side length [i]x[/i]) that are each cut from the corners of the larger square. [b][color=#a64d79]The 4 rectangular pieces that remain[/color][/b] are then folded up to create a rectangular prism (box) with open top. [br][br]You can move the white point to see the different-sized boxes that can be created. [br][br]Use this applet (as needed) to help you as you complete the [b]Box with Open Top [/b]performance task given to you in class today.
– Tim Brzezinski

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