长方体体积练习

长方体体积练习
几何画板及绘图内容加载中,请稍等……
2016-12-15 01:17
本范例演示长方体体积的计算方法。涉及的核心数学概念包括立体几何中的体积计算。通过使用GeoGebra命令如Intersect、Random、Circle等,可以构造出长方体并计算其体积。适合初中及以上学生进行几何作图和体积计算练习。

GeoGebra 命令及参数

  1. Intersect(zAxis, xAxis) → A
  2. Random(1, 11) → A2
  3. Random(1, 11) → B2
  4. Random(1, 11) → C2
  5. Random(1, 4) → a
  6. Circle(A, A2, zAxis) → c
  7. Circle(A, B2, zAxis) → d
  8. Circle(A, C2, yAxis) → e
  9. Intersect(yAxis, c) → B, C_1
  10. Intersect(xAxis, d) → D, E_1
  11. Intersect(zAxis, e) → E, G_1
  12. Plane(A, E, B) → b
  13. OrthogonalLine(B, b) → f
  14. OrthogonalLine(A, b) → g
  15. Plane(A, D, E) → h_2
  16. OrthogonalLine(D, h_2) → i
  17. Intersect(i, f) → C
  18. Polygon(A, B, C, D) → poly1, a_1, b_1, h_1, d_1
  19. Prism(poly1, (-C2)) → j, I_1, edgeAI, edgeBJ, edgeHK, edgeDL, edgeIJ, edgeJK, edgeKL, edgeIL, F, G, J, faceABJI, faceBHKJ, faceDHKL, faceADLI, faceIJKL
  20. Circle(A, h, yAxis) → k
  21. Circle(A, l, xAxis) → p
  22. Circle(A, w, zAxis) → q
  23. Intersect(xAxis, q) → M, N
  24. Intersect(yAxis, p) → O, P
  25. Intersect(zAxis, k) → Q, R
  26. Segment(A, O) → l_1
  27. Segment(Q, A) → m
  28. Segment(A, M) → n
  29. Line(M, l_1) → r
  30. Line(O, n) → s
  31. Intersect(s, r) → S
  32. Polygon(A, O, S, M) → poly2, a_2, o, s_1, m_1
  33. Sequence(Segment[A + (i * (1, 0, 0)), O + (i * (1, 0, 0))], i, 1, w - 1) → list1
  34. Sequence(Segment[A + (i * (0, 1, 0)), M + (i * (0, 1, 0))], i, 1, l - 1) → list2
  35. Sequence(Segment[A + (i * (0, 0, 1)), M + (i * (0, 0, 1))], i, 1, h - 1) → list3
  36. Sequence(Segment[A + (i * (0, 0, 1)), O + (i * (0, 0, 1))], i, 1, h - 1) → list4
  37. Sequence(Segment[M + (i * (0, 0, 1)), S + (i * (0, 0, 1))], i, 1, h - 1) → list5
  38. Sequence(Segment[O + (i * (0, 0, 1)), S + (i * (0, 0, 1))], i, 1, h - 1) → list6
  39. Line(Q, a_2) → t
  40. Line(Q, m_1) → f_1
  41. Line(M, m) → g_1
  42. Line(O, m) → i_1
  43. Intersect(t, i_1) → T
  44. Intersect(g_1, f_1) → U
  45. Line(U, t) → j_1
  46. Line(T, f_1) → k_1
  47. Intersect(j_1, k_1) → V
  48. Polygon(Q, T, V, U) → poly3, q_1, t_1, v, u
  49. Sequence(Segment[Q + (i * (1, 0, 0)), T + (i * (1, 0, 0))], i, 1, w - 1) → list7
  50. Sequence(Segment[Q + (i * (0, 1, 0)), U + (i * (0, 1, 0))], i, 1, l - 1) → list8
  51. Sequence(Segment[A + (i * (0, 0, 1)), O + (i * (0, 0, 1))], i, 1, h - 1) → list9
  52. Sequence(Segment[A + (i * (0, 1, 0)), Q + (i * (0, 1, 0))], i, 1, l - 1) → list10
  53. Sequence(Segment[M + (i * (0, 1, 0)), U + (i * (0, 1, 0))], i, 1, l - 1) → list13
  54. Sequence(Segment[A + (i * (1, 0, 0)), Q + (i * (1, 0, 0))], i, 1, w - 1) → list11
  55. Sequence(Segment[O + (i * (1, 0, 0)), T + (i * (1, 0, 0))], i, 1, w - 1) → list12
  56. Polygon(T, O, A, Q) → poly4, t_2, o_1, a_3, q_2
  57. Polygon(T, V, S, O) → poly5, t_3, v_1, s_2, o_2
  58. Polygon(Q, U, M, A) → poly6, q_3, u_1, m_2, a_4
  59. Polygon(U, V, S, M) → poly7, u_2, v_2, s_3, m_3
  60. Textfield(w_1) → InputBox1

AI 绘图提示语参考

画一个长方体,随机生成底面圆的半径和位置,通过轴的交点和圆的交点确定长方体的顶点,然后绘制长方体的各个面,最后用线段填充长方体的内部,展示其体积计算过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。