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Cylinder and Cone Volume Comparison by singhsaurabhi169

Cylinder and Cone Volume Comparison by singhsaurabhi169
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2017-01-19 19:40
TrigonometryCoordinate GeometrySolid GeometryGeometric Construction
This example dynamically demonstrates the volume calculation process of cylinders and cones, visually showcasing the mathematical relationship between their volumes. Core concepts include volume formulas, geometric properties, and proportional relationships. Construction highlights the use of GeoGebra commands like Vector, Translate, OrthogonalLine, Segment, Mirror, Midpoint, Conic, Line, Intersect, Sequence, and Dilate, along with objects such as B_1, View3D, xa, sinphi, cosphi, ya, sintheta, Zoom, xy, X, a, height, O, radius, costheta, Y, v, Z, w, C, u, A_3, a_2, b_2, c, d, B, e, D, E, h_1, i, F, G, H, I, J, f, j, l. Suitable for high school students learning spatial geometry volume calculations and mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Vector(B_1, Y) → v
  2. Vector(B_1, X) → w
  3. Translate(O, Vector[height * w]) → C
  4. Vector(B_1, Z) → u
  5. Translate(O, Vector[radius * u]) → A_3
  6. OrthogonalLine(View3D, yAxis) → a_2
  7. OrthogonalLine(View3D, xAxis) → b_2
  8. Segment(O, A_3) → d
  9. Translate(O, Vector[radius * v]) → B
  10. Segment(O, B) → e
  11. Mirror(B, O) → D
  12. Mirror(A_3, O) → E
  13. Segment(D, O) → h_1
  14. Segment(E, O) → i
  15. Midpoint(B, A_3) → F
  16. Midpoint(B, F) → G
  17. Midpoint(O, G) → H
  18. Midpoint(H, G) → I
  19. Mirror(I, G) → J
  20. Conic(A_3, J, B, E, D) → f
  21. Segment(C, A_3) → j
  22. Segment(C, B) → l
  23. Segment(C, E) → m_2
  24. Segment(C, D) → n_2
  25. Line(F, O) → p
  26. Midpoint(B, E) → K
  27. Line(K, O) → q
  28. Intersect(f, p) → L, M
  29. Intersect(f, q) → N, P
  30. Segment(C, N) → r
  31. Segment(C, L) → s
  32. Segment(C, P) → t
  33. Segment(C, M) → a1
  34. Segment(C, O) → b1
  35. Vector(O, H1) → z
  36. Translate(f, z) → p1
  37. Translate(C, z) → I1
  38. Vector(H1, I1) → u1
  39. Translate(p1, u1) → q1
  40. Translate(D, z) → J1
  41. Translate(N, z) → K1
  42. Translate(A_3, z) → M1
  43. Translate(M, z) → N1
  44. Translate(L, z) → O1
  45. Translate(E, z) → P1
  46. Translate(P, z) → Q1
  47. Translate(B, z) → R1
  48. Translate(J1, u1) → S1
  49. Translate(K1, u1) → T1
  50. Translate(M1, u1) → U1
  51. Translate(N1, u1) → V1
  52. Translate(R1, u1) → W1
  53. Translate(Q1, u1) → Z1
  54. Translate(O1, u1) → A'2
  55. Translate(P1, u1) → B2
  56. Segment(S1, J1) → l1
  57. Segment(T1, K1) → m1
  58. Segment(U1, M1) → n1
  59. Segment(V1, N1) → r1
  60. Segment(W1, R1) → s1
  61. Segment(Z1, Q1) → t1
  62. Segment(B2, P1) → a2
  63. Segment(A'2, O1) → b2
  64. Segment(I1, H1) → g2
  65. Segment(H1, M1) → h2
  66. Sequence(Translate[p1, Vector[i * u1]], i, 0, 1, o) → L1
  67. Sequence(Dilate[f, i, C], i, 0, 1, o) → L2
  68. Midpoint(h2) → J_1
  69. Midpoint(d) → L_1
  70. Dilate(f, a, C) → f'_2
  71. Translate(p1, Vector[a / 3 * u1]) → p1'
  72. Translate(p1, Vector[1 / 3 * u1]) → p1'_1
  73. Translate(p1, Vector[2 / 3 * u1]) → p1'_2
  74. Sequence(Dilate[f, i, C], i, a, 1, o) → liste11
  75. Sequence(Translate[p1, Vector[i * u1]], i, 0, a / 3, o) → liste1