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Pyramid Volume Construction Demonstration

Pyramid Volume Construction Demonstration
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2020-08-22 16:02
VectorSolid GeometryTransformationGeometric Construction
① This example constructs a pyramid in three‑dimensional space and dynamically computes its volume using GeoGebra. ② It illustrates the formula V = (1/3)·BaseArea·Height, shows how to obtain the base area via vectors, and explains how to locate vertices with coordinate geometry. ③ The construction uses commands such as Cube, Segment, Midpoint, Pyramid, Rotate, Translate, Vector and the Volume command; objects like points a, A, B, C, D, E, F, G, H, faces and edges are created step‑by‑step. ④ Designed for high‑school or early‑university students studying solid geometry, spatial vectors, and mathematical modeling.

GeoGebra Commands & Parameters

  1. Cube(B, C, A) → c, D, faceADHG_1, faceEFGH_1, edgeBD_1, edgeBC_1, edgeAC_1, edgeAD_1, edgeBE_1, edgeDH_1, edgeEH_1, edgeEF_1, E, edgeCF_1, edgeFG_1, edgeAG_1, edgeGH_1, F, G, H, faceACBD_1, faceBDHE_1, faceBCFE_1, faceACFG_1
  2. Segment(B, G) → f
  3. Midpoint(B, G) → I
  4. Pyramid(B, C, F, E, I) → d, faceBCFE, edgeBI_1, edgeCI_1, edgeFI_1, edgeEI_1, faceBCI_1, faceCFI_1, faceEFI_1, faceBEI_1, edgeBC_2, edgeCF_2, edgeEF_2, edgeBE_2
  5. Segment(B, C) → g
  6. Rotate(d, b, g) → d'
  7. Pyramid(C, A, G, F, I) → e, faceACFG_2, edgeCI_2, edgeAI_1, edgeGI_1, edgeFI_2, faceACI_1, faceAGI_1, faceFGI_1, faceCFI_2, edgeAC_2, edgeAG_2, edgeFG_2, edgeCF_3
  8. Pyramid(A, D, H, G, I) → i, faceADHG, edgeAI_2, edgeDI_1, edgeHI_1, edgeGI_2, faceADI_1, faceDHI_1, faceGHI_1, faceAGI_2, edgeAD_2, edgeDH_2, edgeGH_2, edgeAG_3
  9. Segment(A, D) → j
  10. Rotate(i, b, j) → i'
  11. Pyramid(C, A, G, F, I) → h, faceACFG, edgeCI_3, edgeAI_3, edgeGI_3, edgeFI_3, faceACI_2, faceAGI, faceFGI_2, faceCFI, edgeAC_3, edgeAG, edgeFG_3, edgeCF
  12. Segment(C, A) → k
  13. Rotate(h, b, k) → h'
  14. Pyramid(D, B, E, H, I) → l, faceBDHE, edgeDI_2, edgeBI_2, edgeEI_2, edgeHI_2, faceBDI_1, faceBEI, faceEHI_1, faceDHI, edgeBD_2, edgeBE, edgeEH_2, edgeDH
  15. Segment(D, B) → m
  16. Rotate(l, b, m) → l'
  17. Pyramid(H, G, F, E, I) → n, faceEFGH, edgeHI, edgeGI, edgeFI, edgeEI, faceGHI, faceFGI, faceEFI, faceEHI, edgeGH, edgeFG, edgeEF, edgeEH
  18. Segment(E, F) → p
  19. Pyramid(B, C, A, D, I) → q, faceACBD, edgeBI, edgeCI, edgeAI, edgeDI, faceBCI, faceACI, faceADI, faceBDI, edgeBC, edgeAC, edgeAD, edgeBD
  20. Segment(E, F) → r
  21. PointIn(d') → J
  22. Vector(F, J) → u
  23. Translate(Rotate[n, (2 * b), r], u) → o
  24. Volume(i') → volumei'
  25. PointIn(i') → Pointi'
  26. Volume(l') → volumel'
  27. PointIn(l') → Pointl'
  28. Volume(d') → volumed'
  29. PointIn(d') → Pointd'
  30. Volume(o) → volumeo
  31. PointIn(o) → Pointo
  32. Volume(c) → volumec
  33. PointIn(c) → Pointc_1
  34. Volume(h') → volumeh'
  35. PointIn(h') → Pointh'
  36. Volume(q) → volumeq
  37. PointIn(q) → Pointq
  38. Volume(c) → s
  39. PointIn(c) → Pointc
  40. Textfield(a) → InputBox1

AI Drawing Prompt Reference

Draw a three-dimensional solid figure containing multiple pyramids and pyramids. The figure is defined by points A, B, C, D, E, F, G, H. Show how to locate vertices using vectors and coordinate geometry, and calculate volume. The construction order: first create a cube, then create multiple pyramids using rotation and translation, and finally calculate volume.
The prompt above was compiled from the original drawing commands and is for reference only.