平行六面体体积实验

平行六面体体积实验
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2017-04-26 09:45
①本范例演示平行六面体的体积计算与可视化;②涉及核心数学概念包括体积公式、空间几何、三维图形;③构造要点:使用Point, PointIn, Segment, Sphere, Intersect, Line, Distance, Prism, Volume等GeoGebra命令和对象构建平行六面体并计算体积;④适合高中立体几何教学或自学,帮助理解体积计算方法。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. PointIn(Sphere[A, 8.5]) → B
  3. Segment(A, B) → f
  4. Point(yAxis) → C
  5. PointIn(Sphere[C, 4]) → D
  6. Segment(C, D) → g
  7. Sphere(C, D) → a
  8. Intersect(yAxis, a, 2) → E
  9. Segment(C, E) → h
  10. Intersect(yAxis, a) → F, G
  11. Point(h) → H
  12. PointIn(Sphere[H, 1.6]) → I
  13. Segment(H, I) → i
  14. Sphere(H, I) → b
  15. Intersect(zAxis, b) → J, K
  16. Line(C, f) → j
  17. Line(G, i) → k
  18. Line(A, yAxis) → l
  19. Line(B, yAxis) → m
  20. Intersect(l, k) → L
  21. Intersect(l, j) → M
  22. Intersect(j, m) → N
  23. Intersect(j, k) → O
  24. Intersect(m, xOyPlane) → P
  25. Intersect(m, k) → Q
  26. Line(N, zAxis) → n
  27. PointIn(Sphere[N, 1.6]) → R
  28. Segment(N, R) → p
  29. Sphere(N, R) → c
  30. Intersect(n, c) → S, T
  31. Line(T, j) → q
  32. Line(Q, n) → r
  33. Line(T, m) → s
  34. Intersect(r, s) → U
  35. Intersect(n, zAxis) → V
  36. Line(M, n) → t
  37. Line(T, j) → d
  38. Intersect(t, d) → W
  39. Line(W, l) → e
  40. Line(L, t) → f_1
  41. Intersect(e, f_1) → Z
  42. Line(Z, k) → g_1
  43. Segment(M, N) → h_1
  44. Segment(N, Q) → i_1
  45. Segment(Q, L) → j_1
  46. Segment(M, L) → k_1
  47. Segment(M, W) → l_1
  48. Segment(L, Z) → m_1
  49. Segment(N, T) → n_1
  50. Segment(Q, U) → p_1
  51. Segment(W, T) → q_1
  52. Segment(T, U) → r_1
  53. Segment(U, Z) → s_1
  54. Segment(Z, W) → t_1
  55. Distance(Z, U) → distânciaZU
  56. Distance(U, Q) → distânciaUQ
  57. Distance(N, Q) → distânciaNQ
  58. Prism(Z, W, M, L, U) → o, A_1, arestaWZ, arestaMW, arestaLM, arestaLZ, arestaUZ, aresta5, aresta2, aresta1, aresta3, aresta6, B_1, aresta7, aresta4, C_1, faceLMWZ, face4, face3, face1, face2, face5
  59. Volume(o) → volumeo
  60. Point(o) → Pontoo

AI 绘图提示语参考

画一个平行六面体,首先确定三个不共线的点,分别连接它们形成平行四边形的底面,然后通过底面各顶点向上延伸垂直于底面,确定上底面的对应顶点,连接上下底面对应边,完成平行六面体的绘制。接着,计算并可视化其体积,通过底面积乘以高得到体积,并在图中标注相关计算步骤和几何关系,展示空间几何和体积计算方法。
以上提示语为根据原始绘图命令整理而来,仅供参考。