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Volume of Pyramids (Method 2)

Volume of Pyramids (Method 2)
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2019-07-29 11:51
VectorSolid GeometryGeometric Construction
This example demonstrates the construction of pyramids under a cube and the calculation of their volume. Key math concepts include volume formulas, solid geometry, symmetry, and vector operations. The construction uses GeoGebra commands/objects like Cube, Line, Rotate, Segment, Midpoint, Pyramid, Vector, and Translate. Suitable for high school students learning solid geometry and volume calculations, or for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. Cube(A, B, C) → cube, D, faceCDHG_1, faceEFGH_1, edgeAD_1, edgeAB_1, edgeBC_1, edgeCD_1, edgeAE_1, edgeDH_1, edgeEH_1, edgeEF_1, E, edgeBF_1, edgeFG_1, edgeCG_1, edgeGH_1, F, G, H, faceABCD_1, faceADHE_1, faceABFE_1, faceBCGF_1
  2. Line(A, B) → ax1
  3. Rotate(E, fold_unfold, ax1) → E'
  4. Line(E, F) → ax5
  5. Segment(G, A) → f
  6. Midpoint(f) → O
  7. Pyramid(E, F, G, H, O) → Pyr5, faceEFGH, edgecenterE_2, edgecenterF_2, edgecenterG_1, edgecenterH_1, facecenterEF, facecenterFG_1, facecenterGH_1, facecenterEH_1, edgeEF, edgeFG_2, edgeGH_2, edgeEH_2
  8. Pyramid(A, E, F, B, O) → Pyr1, faceABFE, edgeAcenter_1, edgecenterE_1, edgecenterF_1, edgeBcenter_1, faceAcenterE_1, facecenterEF_1, faceBcenterF_1, faceABcenter_1, edgeAE_2, edgeEF_2, edgeBF_2, edgeAB_2
  9. Rotate(Pyr1, fold_unfold, ax1) → Rot1
  10. Vector(E, E') → u
  11. Translate(Rotate[Pyr5, (2 * fold_unfold), ax5], u) → Rot5
  12. Pyramid(B, C, G, F, O) → Pyr2, faceBCGF, edgeBcenter_2, edgeCcenter_1, edgecenterG_2, edgecenterF, faceBCcenter_1, faceCcenterG_1, facecenterFG, faceBcenterF, edgeBC_2, edgeCG_2, edgeFG, edgeBF
  13. Line(B, C) → ax2
  14. Rotate(Pyr2, fold_unfold, ax2) → Rot2
  15. Pyramid(C, D, H, G, O) → Pyr3, faceCDHG, edgeCcenter_2, edgecenterD_1, edgecenterH_2, edgecenterG, faceCcenterD_1, facecenterDH_1, facecenterGH, faceCcenterG, edgeCD_2, edgeDH_2, edgeGH, edgeCG
  16. Line(C, D) → ax3
  17. Rotate(Pyr3, fold_unfold, ax3) → Rot3
  18. Pyramid(D, A, E, H, O) → Pyr4, faceADHE, edgecenterD_2, edgeAcenter_2, edgecenterE, edgecenterH, faceAcenterD_1, faceAcenterE, facecenterEH, facecenterDH, edgeAD_2, edgeAE, edgeEH, edgeDH
  19. Line(D, A) → ax4
  20. Rotate(Pyr4, fold_unfold, ax4) → Rot4
  21. Pyramid(A, B, C, D, O) → Pyr6, faceABCD, edgeAcenter, edgeBcenter, edgeCcenter, edgecenterD, faceABcenter, faceBCcenter, faceCcenterD, faceAcenterD, edgeAB, edgeBC, edgeCD, edgeAD

AI Drawing Prompt Reference

Draw a cube and create four pyramids by connecting the center of the top face to each of its four vertices. Then, reflect and translate these pyramids to the corresponding positions below the cube's faces, forming a composite solid of six pyramids and the cube to demonstrate volume calculation.
The prompt above was compiled from the original drawing commands and is for reference only.