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Intuitive Introduction to Volume by Tim Brzezinski

Intuitive Introduction to Volume by Tim Brzezinski
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2018-11-26 10:17
FunctionSequenceSolid GeometryGeometric Construction
In collections GeoGebra 3D & AR: Geometry Resources & Challenges
This example demonstrates the calculation and visualization of rectangular prism volume. Core math concepts include volume formulas, sequences, functions, percentages, and the Pythagorean theorem. GeoGebra commands used are Sequence, Ray, LENGTH, WIDTH, HEIGHT, etc. Suitable for middle school and above students learning solid geometry and function applications.

GeoGebra Commands & Parameters

  1. Sequence(Cube[(i, 0, 0), (i + 1, 0, 0), Point[Circle[(i + 1, 0, 0), Distance[(i, 0, 0), (i + 1, 0, 0)], Segment[(i, 0, 0), (i + 1, 0, 0)]]]], i, 0, LENGTH - 1, 1) → L_1
  2. Sequence(Cube[(1, i, 0), (1, i + 1, 0), Point[Circle[(1, i + 1, 0), Distance[(1, i, 0), (1, i + 1, 0)], Segment[(1, i, 0), (1, i + 1, 0)]]]], i, 1, WIDTH - 1, 1) → L_2
  3. Sequence(Sequence[Translate[Element[L_1, i], Vector[(0, j)]], j, 1, WIDTH - 1, 1], i, 2, LENGTH, 1) → L_4
  4. Sequence(Translate[L_4, Vector[(0, 0, i)]], i, 1, HEIGHT - 1, 1) → L_5
  5. Sequence(Translate[L_1, Vector[(0, 0, i)]], i, 1, HEIGHT - 1, 1) → L_6
  6. Sequence(Translate[L_2, Vector[(0, 0, i)]], i, 1, HEIGHT - 1, 1) → L_7
  7. Ray((0, 0, 0), (1, 0, 0)) → f
  8. Ray((0, 0, 0), (0, 1, 0)) → g
  9. Ray((0, 0, 0), (0, 0, 1)) → h