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Volume Calculation: Finding Cuboid Volume by Complementary Method

Volume Calculation: Finding Cuboid Volume by Complementary Method
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2024-09-05 16:08
Solid GeometryGeometric ConstructionSlider Animation
In collections Rauminhalt zusammengesetzter Körper - Quader und Würfel
This GeoGebra example demonstrates how to calculate the volume of a cuboid using the complementary method. The core mathematical concept is volume calculation in solid geometry, involving the construction and volume computation of a rectangular prism (Quader). Key construction techniques: using the Volume command to calculate cuboid volume, applying Translate for geometric transformations, implementing answer verification with If conditions, building a 3D coordinate system with CornerThreeD, and generating random questions with Shuffle. The interactive design includes input boxes for learners to enter answers, with automatic correctness checking. Suitable for middle school mathematics curriculum on solid geometry, as well as self-study and practice of volume calculation methods.

GeoGebra Commands & Parameters

  1. Translate({Prism[Polygon[(-2.5, -1.5, -1), (-2.5, -1.5, -1) + (2, 0), (-2.5, -1.5, -1) + (2, 3), (-2.5, -1.5, -1) + (0, 3)], 2]}, Vector[(-0.001, 0, -0.001 - dy)]) → object02
  2. Volume(object02(1)) → sol2
  3. Translate({Prism[Polygon[(-0.5, 1.5), (-0.5, 1.5) + (3, 0), (-0.5, 1.5) + (3, 0, 2), (-0.5, 1.5) + (0, 0, 2)], (-0.5, -1.5)]}, Vector[(0, 0, ((-dz)) / 2 - 1)]) → object122HintWaagrecht1
  4. Element(randomQuestions, Mod[questionCount, Length[randomQuestions]] + 1) → randomQuestion
  5. Element(allQuestions, randomQuestion) → actualQuestion
  6. Shuffle(Sequence[Element[actualQuestion, i], i, 2, numberOfAnswers + 1]) → actualAnswersShuffled, {?, ?, ?, ?, ?, ?}
  7. Element(actualAnswersShuffled, 3) → actualAnswer03
  8. Element(actualAnswersShuffled, 2) → actualAnswer02
  9. Element(actualAnswersShuffled, 1) → actualAnswer01
  10. Element(actualAnswersShuffled, 4) → actualAnswer04
  11. Element(actualAnswersShuffled, 5) → actualAnswer05
  12. Element(actualAnswersShuffled, 6) → actualAnswer06
  13. Element(actualAnswer06, 2) → chk06Expected
  14. Element(actualAnswer05, 2) → chk05Expected
  15. Element(actualAnswer04, 2) → chk04Expected
  16. Element(actualAnswer01, 2) → chk01Expected
  17. Element(actualAnswer02, 2) → chk02Expected
  18. Element(actualAnswer03, 2) → chk03Expected
  19. Cone((0, 0, 2), (0, 0, 5), 1) → figur022kegel, figur012kegel_{2}, figur012kegel_{3}
  20. Cone(((-2.7755575615628914E-17), 0, 1), ((-2.7755575615628914E-17), 0, -3), 1.5) → figur031kegel, figur021kegel_{2}, figur021kegel_{3}
  21. Cone((0, 0, 1), (0, 0, 4), 2.5) → figur042kegel, figur032kegel_{2}, figur032kegel_{3}
  22. Cone((0, 0, 1), (0, 0, 5), 1.5) → figur062kegel, figur062kegel_{2}, figur062kegel_{3}
  23. Textfield(input1) → InputBox1
  24. LaTeX(randomQuestion, true, true) → text1
  25. Remove(l1, {SelectedElement[l1]}) → l2
  26. Textfield(input2) → InputBox2
  27. LaTeX(page, true, true) → text5
  28. Sum({attemptCountInputBox1, attemptCountInputBox2}) → attemptCount
  29. Textfield(input3) → InputBox3
  30. If(page ≟ 2, showQuader2, page ≟ 8, correctInputBox3, true, page ≟ 4, correctInputBox1, page ≟ 5, dy ≥ 1.78, page ≟ 6, correctInputBox2, page ≟ 7, sliderGrey ≥ 0.97) → fixed
  31. CornerThreeD(-1, 11) → viewActual

AI Drawing Prompt Reference

Draw a cuboid and calculate its volume using the complementary method. First, create a cuboid with a base from (-2.5, -1.5, -1) to (-0.5, 1.5, -1), then generate another cuboid by translation. Set up input boxes for users to enter their answers and use conditional statements to check the answers. Finally, build a 3D coordinate system and randomly generate some questions for practice.
The prompt above was compiled from the original drawing commands and is for reference only.