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Volume of Pyramids (Method 1) by Bed Prasad Dhakal

Volume of Pyramids (Method 1) by Bed Prasad Dhakal
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2019-12-08 20:34
Solid GeometryGeometric Construction
This example demonstrates the construction of pyramids within a cube and uses it to illustrate the calculation of pyramid volume. Key mathematical concepts include the volume formula for pyramids in solid geometry. It utilizes GeoGebra commands such as Cube, Pyramid, Line, and Rotate to construct the pyramid's faces and edges. Suitable for middle school and above students studying solid geometry and volume calculations.

GeoGebra Commands & Parameters

  1. Cube(A, B, C) → cube, D, faceCDHG_1, faceEFGH, 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, faceBCGF
  2. Pyramid(A, B, C, D, F) → Pyr1, faceABCD, edgeAF_1, edgeBF, edgeCF_1, edgeDF_1, faceABF, faceBCF, faceCDF_1, faceADF_1, edgeAB, edgeBC, edgeCD_2, edgeAD_2
  3. Pyramid(A, E, H, D, F) → Pyr2, faceADHE, edgeAF, edgeEF, edgeFH_1, edgeDF_2, faceAEF, faceEFH, faceDFH_1, faceADF, edgeAE, edgeEH, edgeDH_2, edgeAD
  4. Pyramid(D, C, G, H, F) → Pyr3, faceCDHG, edgeDF, edgeCF, edgeFG, edgeFH, faceCDF, faceCFG, faceFGH, faceDFH, edgeCD, edgeCG, edgeGH, edgeDH
  5. Line(A, D) → ax2
  6. Line(C, D) → ax3
  7. Rotate(Pyr2, (-fold_unfold), ax2) → Rot2
  8. Rotate(Pyr3, fold_unfold, ax3) → Rot3

AI Drawing Prompt Reference

Draw a cube. Inside it, construct three pyramids sharing a common vertex at one corner of the cube, each using one of the three adjacent faces of the cube as its base, so that together they fill the cube. Then draw two lines along an edge of the base and a vertical edge of the cube as rotation axes. Rotate two of the pyramids outward around these axes by a certain angle to unfold them from the cube, showing the relationship between pyramid volume and cube volume. The figure includes the cube, three pyramids, two rotation axes, and the rotated positions of the pyramids.
The prompt above was compiled from the original drawing commands and is for reference only.