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Right Prism and Volume

Right Prism and Volume
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2012-02-09 02:20
Coordinate GeometrySolid GeometryGeometric Construction
In collections Area, Surface Area, Volume--Nets
This example demonstrates the geometric construction of a right prism and its volume calculation. Key mathematical concepts include the definition of a prism in solid geometry, volume formulas, and the use of GeoGebra for geometric construction. By using commands like Sequence, Element, Point, Polygon, Segment, users can dynamically explore the construction process of the prism.

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