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Cone Volume Calculation Demo

Cone Volume Calculation Demo
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2018-07-09 20:39
Solid GeometryCalculusGeometric Construction
This example demonstrates the calculation process and formula verification of cone volume. It involves core mathematical concepts such as the cone volume formula, solid geometry, and integral concepts. The construction uses GeoGebra commands like Circle, Point, Line, Intersect, Ellipse, Segment, Rotate, Vector, Translate, OrthogonalLine, Angle to build the cone model and calculate its volume. Suitable for high school solid geometry teaching and introductory mathematical modeling.

GeoGebra Commands & Parameters

  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