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Right Prisms and Volumes

Right Prisms and Volumes
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2015-09-04 05:48
TrigonometrySolid Geometry
This example demonstrates the construction of right prisms and their volume calculations. Key mathematical concepts include solid geometry, volume computation, and the application of trigonometric functions. Using GeoGebra commands such as Sequence, Element, and Point, the construction process of the prism can be dynamically displayed. Suitable for high school mathematics education or students learning solid geometry.

GeoGebra Commands & Parameters

  1. Sequence(Mat * Element[cube, k], k, 1, 8) → cube'
  2. Element(Element[AE, 3], 1) → droite
  3. Sequence((Element[cube', k, 1, 1], Element[cube', k, 2, 1]), k, 1, 8) → listepoints
  4. Point(listepoints) → A
  5. Point(listepoints) → E
  6. Point(listepoints) → C_1
  7. Point(listepoints) → D
  8. Polygon(A, E, C_1, D) → poly1, a_1, b, c_1, d
  9. Point(listepoints) → B
  10. Point(listepoints) → F
  11. Point(listepoints) → G
  12. Point(listepoints) → H
  13. Polygon(B, F, G, H) → poly2, e, f, g, h
  14. Point(listepoints) → C
  15. Polygon(F, C, A, B) → poly3, f_1, i, a_2, b_1
  16. Element(AB, 3, 1) → avant
  17. Polygon(C_1, G, H, E) → poly4, c_2, g_1, h_1, e_1
  18. Element(AC, 3, 1) → dessus
  19. Polygon(F, C, C_1, G) → poly5, f_2, c_3, c_4, g_2
  20. Polygon(A, B, H, E) → poly6, a_3, b_2, h_2, e_2
  21. Segment(E, A) → c
  22. Segment(A, C) → j
  23. Segment(A, B) → k
  24. Segment(C, C_1) → l
  25. Segment(C_1, E) → m
  26. Segment(H, E) → n
  27. Segment(A, B) → p
  28. Segment(B, H) → q
  29. Segment(H, E) → r
  30. Segment(H, G) → s
  31. Segment(B, F) → t
  32. Segment(G, C_1) → d_1
  33. Segment(F, G) → i_1
  34. Segment(F, C) → j_1
  35. Sequence(Sequence[Sequence[Polygon[Translate[A, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[E, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[C_1, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[D, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste1
  36. Sequence(Sequence[Sequence[Polygon[Translate[B, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[F, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[G, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[H, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste2
  37. Sequence(Sequence[Sequence[Polygon[Translate[F, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[C, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[A, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[B, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste3
  38. Sequence(Sequence[Sequence[Polygon[Translate[C_1, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[G, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[H, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[E, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste4
  39. Sequence(Sequence[Sequence[Polygon[Translate[F, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[C, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[C_1, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[G, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste5
  40. Sequence(Sequence[Sequence[Polygon[Translate[A, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[B, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[H, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]], Translate[E, Vector[k * Vector[A, E] + l * Vector[A, B] + i * Vector[A, D]]]], k, 0, u], l, 0, k_1], i, 0, l_1) → liste6