积极 AI Logo 积极 AI

长方体体积的几何拼接

长方体体积的几何拼接
几何画板及绘图内容加载中，请稍等……
2016-02-29 21:48
解析几何立体几何几何作图
所属专题 Area, Surface Area, Volume, Cross Section, 3D Geometry: Surface Area & Volume Geometry: Surface Area & Volume Geometry: Surface Area & Volume GA Chapter 11: Surface Area and Volume
本示例通过动态拼接立方体来展示长方体的体积计算方法。核心数学概念包括体积计算和立方体的几何特性。通过使用GeoGebra命令如Random, Sequence, Surface, Prism等，可以直观地展示长方体的构造过程。适合小学高年级或初中学生学习几何和体积概念。

GeoGebra 命令及参数

  1. Random(1, 13) → a
  2. Sequence(Plane[x + (0 * z) = k], k, 1, a, 1) → list2
  3. Random(1, 13) → b
  4. Sequence(Plane[y + (0 * z) = k], k, 1, b, 1) → list1
  5. Random(1, 10) → h
  6. Surface(j, k, h, j, 0, a, k, 0, b) → d
  7. Surface(j, k, 0, j, 0, a, k, 0, b) → A2
  8. Surface(j, k, C2 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D2
  9. Surface(j, k, C3 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D3
  10. Surface(j, k, C4 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D4
  11. Surface(j, k, C5 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D5
  12. Surface(j, k, C6 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D6
  13. Surface(j, k, C7 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D7
  14. Surface(j, k, C8 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D8
  15. Surface(j, k, C9 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D9
  16. Surface(j, k, C10 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D10
  17. Surface(j, k, C11 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D11
  18. Surface(j, k, C12 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D12
  19. Surface(j, k, C13 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D13
  20. Surface(j, k, C14 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D14
  21. Surface(j, k, C15 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D15
  22. Surface(j, k, C16 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D16
  23. Surface(j, k, C17 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D17
  24. Surface(j, k, C18 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D18
  25. Surface(j, k, C19 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D19
  26. Surface(j, k, C20 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D20
  27. Surface(j, k, C21 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D21
  28. Surface(j, k, C22 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D22
  29. Surface(j, k, C23 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D23
  30. Surface(j, k, C24 / n, j, -0.03, row + 0.03, k, -0.03, col + 0.03) → D24
  31. Prism(A, B, C, D, A, E) → e, F, faceAAEI, faceEFGHI, edgeAB, edgeBC, edgeCD, edgeAD, edgeAA, edgeAE, edgeBF, edgeCG, G, edgeDH, edgeAI, edgeEF, edgeFG, edgeGH, edgeHI, edgeEI, H, I, faceAADCB, faceABFE, faceBCGF, faceCDHG, faceADHI
  32. Random(0, 10) → c
  33. Random(1, 13) → a_1
  34. Random(1, 13) → b_1
  35. Surface(j, C1, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F1
  36. Surface(j, C2, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F2
  37. Surface(j, C3, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F3
  38. Surface(j, C4, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F4
  39. Surface(j, C5, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F5
  40. Surface(j, C6, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F6
  41. Surface(j, C7, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F7
  42. Surface(j, C8, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F8
  43. Surface(j, C9, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F9
  44. Surface(j, C10, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F10
  45. Surface(j, C11, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F11
  46. Surface(j, C12, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F12
  47. Surface(j, C13, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F13
  48. Surface(j, C14, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F14
  49. Surface(j, C15, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F15
  50. Surface(j, C16, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F16
  51. Surface(j, C17, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F17
  52. Surface(j, C18, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F18
  53. Surface(j, C19, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F19
  54. Surface(j, C20, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F20
  55. Surface(j, C21, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F21
  56. Surface(j, C22, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F22
  57. Surface(j, C23, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F23
  58. Surface(j, C24, k, j, -0.03, row + 0.03, k, -0.03, layer + 0.03) → F24
  59. Surface(C1, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E1
  60. Surface(C2, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E2
  61. Surface(C3, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E3
  62. Surface(C4, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E4
  63. Surface(C5, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E5
  64. Surface(C6, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E6
  65. Surface(C7, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E7
  66. Surface(C8, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E8
  67. Surface(C9, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E9
  68. Surface(C10, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E10
  69. Surface(C11, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E11
  70. Surface(C12, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E12
  71. Surface(C13, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E13
  72. Surface(C14, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E14
  73. Surface(C15, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E15
  74. Surface(C16, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E16
  75. Surface(C17, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E17
  76. Surface(C18, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E18
  77. Surface(C19, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E19
  78. Surface(C20, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E20
  79. Surface(C21, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E21
  80. Surface(C22, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E22
  81. Surface(C23, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E23
  82. Surface(C24, k, j, j, -0.03, layer + 0.03, k, -0.03, col + 0.03) → E24