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Volume of Pyramid

Volume of Pyramid
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2020-10-06 23:47
Solid GeometryGeometric Construction
This example demonstrates how to calculate the volume of a pyramid using geometric construction. Key mathematical concepts include the volume formula for a pyramid in solid geometry. Using GeoGebra commands such as Polygon, Cube, and Pyramid, the construction of the pyramid and the calculation of its volume are illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Polygon(D, B, 4, xOyPlane) → poly1, f, g, h, i, F, G
  2. Cube(poly1, true) → a, H, edgeDH_{1}, edgeGK_{1}, edgeHK_{1}, edgeHI_{1}, edgeBI_{1}, edgeIJ_{1}, edgeFJ_{1}, edgeJK_{1}, I, J, K, faceDGKH, faceBDHI_{1}, faceBFJI_{1}, faceFGKJ, faceHIJK
  3. Pyramid(D, B, F, G, K) → b, faceBDGF, edgeDK_{1}, edgeBK_{1}, edgeFK_{1}, edgeGK, faceBDK_{1}, faceBFK_{1}, faceFGK, faceDGK, edgeBD_{1}, edgeBF_{1}, edgeFG, edgeDG
  4. Pyramid(D, B, I, H, K) → c, faceBDHI, edgeDK, edgeBK_{2}, edgeIK_{1}, edgeHK, faceBDK, faceBIK_{1}, faceHIK, faceDHK, edgeBD, edgeBI_{2}, edgeHI, edgeDH
  5. Line(D, B) → j
  6. Rotate(c, α, j) → c'
  7. Pyramid(B, F, J, I, K) → d, faceBFJI, edgeBK, edgeFK, edgeJK, edgeIK, faceBFK, faceFJK, faceIJK, faceBIK, edgeBF, edgeFJ, edgeIJ, edgeBI
  8. Point(edgeBK) → L
  9. Pyramid(faceBFJI, J) → e, faceBFJ, faceFJJ, faceIJJ, faceBIJ, edgeBJ, edgeFJ, edgeJJ, edgeIJ
  10. Point(edgeFJ) → M
  11. Line(B, F) → k
  12. Rotate(d, α, k) → d'

AI Drawing Prompt Reference

Draw a geometric figure consisting of a cube with pyramids attached. The cube serves as the base structure, and pyramids are connected to different faces of the cube. The construction order should be: first draw the cube, then build the first pyramid using cube vertices, rotate a pyramid, and finally construct a second pyramid based on the rotated pyramid. The figure should clearly show the relationship between the pyramids and the cube, illustrating the concept of volume calculation.
The prompt above was compiled from the original drawing commands and is for reference only.