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计算组合体的体积

计算组合体的体积
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2024-09-05 16:17
立体几何几何作图
所属专题 Rauminhalt zusammengesetzter Körper - Quader und Würfel
本范例演示如何通过组合几何体来计算其总体积。核心数学概念包括体积计算和几何体组合。使用了 GeoGebra 命令如 Shuffle、Element、Cone、Textfield 等进行几何体的构造。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Shuffle(1…numberOfQuestions) → randomQuestions, {3, 8, 4, 9, 2, 13, 12, 5, 10, 1, 11, 7, 6}
  2. Element(randomQuestions, Mod[questionCount, Length[randomQuestions]] + 1) → randomQuestion
  3. Element(allQuestions, randomQuestion) → actualQuestion
  4. Shuffle(Sequence[Element[actualQuestion, i], i, 2, numberOfAnswers + 1]) → actualAnswersShuffled, {{"Quader, aber kein Würfel", false}, {"Kugel", true}, {"Zylinder", false}, {"Pyramide", false}, {"Würfel", false}, {"Kegel", true}}
  5. Element(actualAnswersShuffled, 3) → actualAnswer03
  6. Element(actualAnswersShuffled, 2) → actualAnswer02
  7. Element(actualAnswersShuffled, 1) → actualAnswer01
  8. Element(actualAnswersShuffled, 4) → actualAnswer04
  9. Element(actualAnswersShuffled, 5) → actualAnswer05
  10. Element(actualAnswersShuffled, 6) → actualAnswer06
  11. Element(actualAnswer06, 2) → chk06Expected
  12. Element(actualAnswer05, 2) → chk05Expected
  13. Element(actualAnswer04, 2) → chk04Expected
  14. Element(actualAnswer01, 2) → chk01Expected
  15. Element(actualAnswer02, 2) → chk02Expected
  16. Element(actualAnswer03, 2) → chk03Expected
  17. Cone((0, 0, 2), (0, 0, 5), 1) → figur022kegel, figur012kegel_{2}, figur012kegel_{3}
  18. Cone(((-2.7755575615628914E-17), 0, 1), ((-2.7755575615628914E-17), 0, -3), 1.5) → figur031kegel, figur021kegel_{2}, figur021kegel_{3}
  19. Cone((0, 0, 1), (0, 0, 4), 2.5) → figur042kegel, figur032kegel_{2}, figur032kegel_{3}
  20. Cone((0, 0, 1), (0, 0, 5), 1.5) → figur062kegel, figur062kegel_{2}, figur062kegel_{3}
  21. Textfield(input1) → InputBox1
  22. Textfield(red) → InputBox2
  23. Textfield(green) → InputBox3
  24. Textfield(blue) → InputBox4
  25. LaTeX(randomQuestion, true, true) → text1
  26. CornerThreeD(-1, 11) → viewActual
  27. Translate({Prism[Polygon[(2, -1.001), (2, -1.001) + (1.002, 0), (2, -1.001) + (1.002, 2), (2, -1.001) + (0, 2)], (2, -1.001, 5)]}, Vector[(0.001, 0, 0)]) → object041Hint2
  28. Translate({Prism[Polygon[(-3.5, 1), (-3.5, 1) + (5, 0), (-3.5, 1) + (5, 0, 2), (-3.5, 1) + (0, 0, 2)], (-3.5, -1)]}, Vector[(0, 0, -0.001)]) → object112HintPrism1
  29. Translate({Prism[Polygon[(-0.5, 1, 3), (-0.5, 1, 3) + (4, 0), (-0.5, 1, 3) + (4, 0, 3), (-0.5, 1, 3) + (0, 0, 3)], (-0.5, -1, 3)]}, Vector[(0, 0, 0.001)]) → object112HintsPrism3
  30. Translate({Prism[Polygon[(-2.5, 1.5, 2), (-2.5, 1.5, 2) + (5, 0), (-2.5, 1.5, 2) + (5, 0, 3), (-2.5, 1.5, 2) + (0, 0, 3)], (-2.5, -1.5, 2)]}, Vector[(0, 0, 0.001)]) → object122HintPrism2
  31. Translate({Prism[Polygon[(-2.5, 1.5), (-2.5, 1.5) + (2, 0), (-2.5, 1.5) + (2, 0, 2), (-2.5, 1.5) + (0, 0, 2)], (-2.5, -1.5)]}, Vector[(-0, 0, -0)]) → object121HintPrism1
  32. Translate({Prism[Polygon[(2, 1.5, 5), (2, 1.5, 5) + (3, 0), (2, 1.5, 5) + (3, 0, 2), (2, 1.5, 5) + (0, 0, 2)], (2, -1.5, 5)]}, Vector[(0.001, 0, 0.001)]) → object091HintPrism
  33. Midpoint(A, B) → C
  34. LineBisector(A, B) → f
  35. Midpoint(D, E) → F

AI 绘图提示语参考

请绘制一个由多个锥体和棱柱组合而成的立体图形。这些锥体和棱柱通过平移和连接组合在一起，形成一个复合固体。图形中包含不同高度的锥体和棱柱，可能用于展示体积计算。确保图形清晰，形状准确，比例协调。
以上提示语为根据原始绘图命令整理而来，仅供参考。