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Parallelepiped Volume Experiment

Parallelepiped Volume Experiment
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2017-04-26 09:45
Solid GeometryGeometric Construction
This example demonstrates the calculation and visualization of the volume of a parallelepiped. It involves core mathematical concepts such as volume formulas, spatial geometry, and three-dimensional shapes. Construction highlights include using commands and objects like Point, PointIn, Segment, Sphere, Intersect, Line, Distance, Prism, Volume in GeoGebra to build the parallelepiped and compute its volume. Suitable for high school geometry teaching or self-study to understand volume calculation methods.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a parallelepiped by first determining three non-collinear points and connecting them to form a parallelogram base. Extend perpendicular lines from each vertex of the base upward to define the corresponding vertices of the top face, then connect the corresponding edges of the top and bottom faces to complete the shape. Calculate and visualize the volume by multiplying the base area by the height, and label the relevant calculation steps and geometric relationships in the diagram to demonstrate spatial geometry and volume calculation methods.
The prompt above was compiled from the original drawing commands and is for reference only.