组合体体积计算应用题

组合体体积计算应用题
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2023-01-02 22:32
本范例演示如何计算由两个长方体组成的空间模型体积。涉及的核心数学概念是组合体体积计算。作图要点包括使用Shuffle、Element、Textfield、Polygon、Corner、Translate、Circle、Intersect、Segment、Line、Midpoint、Text等GeoGebra命令和对象。适合4-5年级学生学习如何解决实际生活中的组合体体积问题。

GeoGebra 命令及参数

  1. Shuffle(Sequence[5]) → randomList1, {1, 3, 4, 5, 2}
  2. Element(randomList1, Mod[countQuestion, Length[randomList1]] + 1) → randomNum1
  3. Shuffle(Sequence[1, Min[100 / randomNum1, randomNum1 + 5]]) → randomList2, {6, 1, 5, 2, 4, 3}
  4. Element(randomList2, Mod[countQuestion, Length[randomList2]] + 1) → randomNum2
  5. Shuffle(Sequence[1, Min[100 / ((randomNum1 * randomNum2)), randomNum1 + 5]]) → randomList4, {2, 5, 6, 4, 1, 3}
  6. Shuffle(Sequence[1, Min[100 / randomNum1, randomNum1 + 5]] \ {randomNum2}) → randomList3, {2, 1, 5, 4, 3}
  7. Element(randomList3, Mod[countQuestion, Length[randomList3]] + 1) → randomNum3
  8. Element(randomList4, Mod[countQuestion, Length[randomList4]] + 1) → randomNum4
  9. Shuffle(Sequence[1, Min[100 / ((randomNum1 * randomNum3)), randomNum1 + 5]] \ {randomNum4}) → randomList5, {1, 6, 3, 5, 4}
  10. Textfield(input1) → InputBox1
  11. Element(randomList5, Mod[countQuestion, Length[randomList5]] + 1) → randomNum5
  12. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  13. Corner(5) → layoutAppSize
  14. Textfield() → InputBox2
  15. Corner(5) → AppSize
  16. Translate(hguideline, Vector[(Vector[Corner[4], Corner[1]] / 500 * 24)]) → hguideline'
  17. Circle(A, 4) → c
  18. Intersect(c, xAxis) → B, C
  19. Segment(A, C) → f
  20. Circle(A, modelWidth1) → d
  21. Intersect(d, f, 1) → D
  22. Circle(C, modelH2) → e
  23. Intersect(e, eq1, 1) → E
  24. Line(A, eq1) → g
  25. Line(E, f) → h
  26. Line(D, eq1) → i
  27. Intersect(h, i) → F
  28. Line(C, G) → j
  29. Circle(C, modelL) → k
  30. Intersect(k, j, 2) → H
  31. Line(H, eq1) → l
  32. Line(E, j) → m
  33. Intersect(l, m) → I
  34. Circle(A, modelH1) → p
  35. Intersect(p, g, 1) → J
  36. Line(F, m) → n
  37. Line(I, f) → q
  38. Intersect(n, q) → K
  39. Line(J, f) → r
  40. Intersect(i, r) → L
  41. Polygon(F, E, I, K) → q1, f_1, e_1, i_1, k_1
  42. Polygon(F, D, C, E) → q2, f_2, d_1, c_1, e_2
  43. Polygon(C, H, I, E) → q3, c_2, h_1, i_2, e_3
  44. Line(J, c_2) → s
  45. Translate(L, Vector[C, H]) → L'
  46. Translate(D, Vector[C, H]) → D'
  47. Polygon({D, D', L', L}) → q4
  48. Translate(L', Vector[D, A]) → L''
  49. Polygon({J, L, L', L''}) → q5
  50. Polygon({J, A, D, L}) → q6
  51. Midpoint(A, D) → M
  52. Midpoint(C, D) → N
  53. Text(labelH2, Midpoint[h_1], true, true, 1, 1) → text4
  54. Text(labelW1, M, true, true, -1, -1) → text2
  55. Text(labelW2, N, true, true, -1, -1) → text3
  56. Text(labelH1, Midpoint[A, J], true, true, -1, 0) → text5
  57. Text(labelL, Midpoint[C, H], true, true, 1, -1) → text6
  58. Circle(D, HintH1) → t
  59. Intersect(t, i) → O, P
  60. Line(O, h) → a
  61. Intersect(a, g) → Q
  62. Polygon(D, O, Q, A) → q1H, d_2, o, q_1, a_1
  63. Translate(O, Vector[D, D']) → O'
  64. Polygon(D, D', O', O) → q2H, d_3, d', o', o_1
  65. Translate(q5, Vector[J, Q]) → q3H
  66. Translate(D, (0, HintH2)) → D'_{1}
  67. Translate(C, (0, HintH2)) → C'
  68. Polygon(D, C, C', D'_{1}) → q4H, d_4, c_3, c', d'_{1}
  69. Translate(H, (0, HintH2)) → H'
  70. Polygon(C, H, H', C') → q5H, c_4, h_2, h', b
  71. Translate(F, Vector[F, D'_{1}]) → F'
  72. Translate(E, Vector[F, D'_{1}]) → E'
  73. Translate(I, Vector[F, D'_{1}]) → I'
  74. Translate(K, Vector[F, D'_{1}]) → K'
  75. Polygon(F', E', I', K') → q6H, f', e', i', k'

AI 绘图提示语参考

这是一个由两个右直角棱柱组成的复合体积模型。图形包含一个边界矩形,以及一些圆、线段和交点,用于表示体积计算。构造顺序包括随机选择尺寸,绘制边界矩形,创建圆和线段,计算交点,最后绘制一些平行四边形。图形可能用于教学演示,帮助学生理解复合体积的概念。
以上提示语为根据原始绘图命令整理而来,仅供参考。