积极 AI Logo 积极 AI

通过GeoGebra分解复合体计算体积

通过GeoGebra分解复合体计算体积
几何画板及绘图内容加载中，请稍等……
2023-03-16 17:06
立体几何几何作图
所属专题 Ⓔ Volumen zusammengesetzter Körper aus Quader und Würfel
本范例演示如何利用GeoGebra工具分解复合立体图形并计算其体积。核心数学概念包括立体几何中的体积计算、复合体分解原理以及单位立方体的应用。作图要点涉及使用Translate、If、Element、Shuffle、Sum、CornerThreeD等GeoGebra命令构建三维模型，并利用对象122、dz、dx等元素进行空间变换。适合小学中高年级学生用于理解体积计算方法，适用于课堂教学或自主学习场景。

GeoGebra 命令及参数

  1. Translate({Prism[Polygon[(-0.5, 1.5, -1), (-0.5, 1.5, -1) + (3, 0), (-0.5, 1.5, -1) + (3, -3), (-0.5, 1.5, -1) + (0, -3)], (-0.5, 1.5, 5)]}, Vector[(dx / 2 + 0.001, 0, 0)]) → object122HintSenkrecht1
  2. 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
  3. Translate({Prism[Polygon[(-2.5, 1.5, 1), (-2.5, 1.5, 1) + (5, 0), (-2.5, 1.5, 1) + (5, 0, 4), (-2.5, 1.5, 1) + (0, 0, 4)], (-2.5, -1.5, 1)]}, Vector[(dx, 0, dz / 2 + 0.001)]) → object122HintWaagrecht2
  4. Translate({Prism[Polygon[(-0.5, 1.5, 1), (-0.5, 1.5, 1) + (0, -3), (-0.5, 1.5, 1) + (-2, -3), (-0.5, 1.5, 1) + (-2, 0)], (-0.5, 1.5, 5)]}, Vector[(((-dx)) / 2, 0, 0)]) → object122HintSenkrecht2
  5. If(SelectedIndex[l1] ≟ 2, Volume[object122HintWaagrecht1(1)], Volume[object122HintSenkrecht1(1)]) → sol2
  6. If(SelectedIndex[l1] ≟ 2, Volume[object122HintWaagrecht2(1)], Volume[object122HintSenkrecht2(1)]) → sol1
  7. Element(randomQuestions, Mod[questionCount, Length[randomQuestions]] + 1) → randomQuestion
  8. Element(allQuestions, randomQuestion) → actualQuestion
  9. Shuffle(Sequence[Element[actualQuestion, i], i, 2, numberOfAnswers + 1]) → actualAnswersShuffled, {?, ?, ?, ?, ?, ?}
  10. Element(actualAnswersShuffled, 3) → actualAnswer03
  11. Element(actualAnswersShuffled, 2) → actualAnswer02
  12. Element(actualAnswersShuffled, 1) → actualAnswer01
  13. Element(actualAnswersShuffled, 4) → actualAnswer04
  14. Element(actualAnswersShuffled, 5) → actualAnswer05
  15. Element(actualAnswersShuffled, 6) → actualAnswer06
  16. Element(actualAnswer06, 2) → chk06Expected
  17. Element(actualAnswer05, 2) → chk05Expected
  18. Element(actualAnswer04, 2) → chk04Expected
  19. Element(actualAnswer01, 2) → chk01Expected
  20. Element(actualAnswer02, 2) → chk02Expected
  21. Element(actualAnswer03, 2) → chk03Expected
  22. Cone((0, 0, 2), (0, 0, 5), 1) → figur022kegel, figur012kegel_{2}, figur012kegel_{3}
  23. Cone(((-2.7755575615628914E-17), 0, 1), ((-2.7755575615628914E-17), 0, -3), 1.5) → figur031kegel, figur021kegel_{2}, figur021kegel_{3}
  24. Cone((0, 0, 1), (0, 0, 4), 2.5) → figur042kegel, figur032kegel_{2}, figur032kegel_{3}
  25. Cone((0, 0, 1), (0, 0, 5), 1.5) → figur062kegel, figur062kegel_{2}, figur062kegel_{3}
  26. Textfield(input1) → InputBox1
  27. LaTeX(randomQuestion, true, true) → text1
  28. Remove(l1, {SelectedElement[l1]}) → l2
  29. Textfield(input2) → InputBox2
  30. LaTeX(page, true, true) → text5
  31. Sum({attemptCountInputBox1, attemptCountInputBox2}) → attemptCount
  32. Textfield(input3) → InputBox3
  33. If(page ≟ 2, page2CheckboxChanged, page ≟ 7, SelectedIndex[l2] ≠ 1, true, page ≟ 3, dz ≥ 2 ∨ dx ≥ 2, page ≟ 4, correct, page ≟ 5, dz ≟ 0 ∧ dx ≟ 0, page ≟ 6, correctInputBox3) → fixed
  34. CornerThreeD(-1, 11) → viewActual
  35. SelectedIndex(l1Page8) → selectedIndexPage8
  36. SelectedIndex(l1) → a

AI 绘图提示语参考

画一个三维几何体的分解体积示意图：先在空间中放置一个棱柱状主体，并用两种平移得到若干分块，呈现不同方向的长方体/棱柱切分。让其中一个分块沿水平方向偏移形成组合结构，另一个分块沿竖直方向偏移以体现不同高度。随后把视角调整到能同时看到整体与各分块的位置关系。再在同一画面中添加若干带有圆锥外形的几何体作为对照，圆锥的顶点在同一竖直轴线上，不同圆锥具有不同高度与半径，并用它们支撑体积计算的直观理解。
以上提示语为根据原始绘图命令整理而来，仅供参考。