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圆锥体积计算演示

圆锥体积计算演示
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2018-07-09 20:39
立体几何微积分几何作图
①本范例演示圆锥体积的计算过程与公式验证；②涉及核心数学概念包括圆锥体积公式、立体几何、积分概念；③作图要点：使用Circle, Point, Line, Intersect, Ellipse, Segment, Rotate, Vector, Translate, OrthogonalLine, Angle等GeoGebra命令构建圆锥模型并计算体积；④适合高中立体几何教学和数学建模入门学习。

GeoGebra 命令及参数

  1. Circle(A, r) → c
  2. Point(c) → B
  3. Line(B, A) → a
  4. Intersect(c, a) → C, D
  5. Point(c) → E
  6. Line(E, A) → b
  7. Point(b) → F
  8. Point(b) → G
  9. Ellipse(B, D, G) → d
  10. Point(Circle[A, h]) → H
  11. Segment(A, H) → e
  12. Rotate(A, 90*°, A) → A'
  13. Rotate(H, 90*°, A) → H'
  14. Segment(A', H') → e'
  15. Vector(A, H') → u
  16. Translate(d, u) → d'
  17. OrthogonalLine(B, e) → f
  18. OrthogonalLine(H, e) → g
  19. Intersect(d', f) → I, J
  20. Intersect(d', g) → K, L
  21. Segment(B, I) → i
  22. Segment(H, K) → j
  23. Segment(A, D) → k
  24. OrthogonalLine(D, k) → l
  25. Intersect(d', l) → N, O
  26. Segment(O, D) → m
  27. Circle(P, r) → p
  28. Point(p) → Q
  29. Line(P, Q) → n
  30. OrthogonalLine(P, n) → q
  31. Rotate(P, 30*°, Q) → P'
  32. Angle(P, Q, P') → α
  33. Line(Q, P') → s
  34. Rotate(P, 330*°, Q) → P'_1
  35. Angle(P'_1, Q, P) → β
  36. Line(Q, P'_1) → t
  37. Intersect(t, s) → R
  38. Intersect(q, t) → S
  39. Intersect(s, q) → T
  40. Line(P, Q) → a_1
  41. OrthogonalLine(P, a_1) → b_1
  42. Rotate(P, 15*°, Q) → P'_2
  43. Angle(P, Q, P'_2) → γ
  44. Rotate(P, 345*°, Q) → P'_3
  45. Angle(P'_3, Q, P) → δ
  46. Line(Q, P) → c_1
  47. Line(Q, P) → d_1
  48. Intersect(p, d_1) → U, V
  49. Ellipse(V, Q, W) → e_1
  50. Segment(P, Q) → f_1
  51. Point(e_1) → A_1
  52. Point(Circle[P, h]) → Z
  53. Segment(P, Z) → g_1
  54. Rotate(Z, 90*°, P) → Z'
  55. Segment(P, Z') → h_1
  56. Segment(V, Z') → i_1
  57. Segment(Z', Q) → j_1