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Cube Volume Demonstration and Geometric Construction

Cube Volume Demonstration and Geometric Construction
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2012-09-12 14:52
PolygonSequenceSolid GeometryTransformationGeometric Construction
① This example shows how to build a cube in GeoGebra and visually demonstrate its volume calculation. ② Core mathematical concepts include the solid‑geometry volume formula for a cube, geometric transformations such as dilation and translation, and the principles of constructing polygons and polyhedra. ③ Construction highlights: basic commands Point, Segment, and Polygon create vertices A‑H and the four face polygons (poly1‑poly4); parameters a, b, c control edge length, enabling dynamic linkage between side length and volume. ④ Suitable for middle‑school and high‑school solid‑geometry lessons, geometric construction practice, and intuitive verification of the volume formula.

GeoGebra Commands & Parameters

  1. Point(Circle[A, Sisi]) → B
  2. Point(Circle[A, Sisi]) → E
  3. Point(Circle[A, Sisi]) → D
  4. Point(Circle[D, Sisi]) → H
  5. Point(Circle[D, Sisi]) → C
  6. Point(Circle[H, Sisi]) → G
  7. Segment(E, H) → sisi
  8. Segment(C, B) → a_0
  9. Segment(A, B) → a_1
  10. Segment(A, E) → a_2
  11. Segment(A, D) → a_3
  12. Segment(D, H) → a_4
  13. Segment(D, C) → a_5
  14. Segment(C, G) → a_6
  15. Segment(H, G) → a_7
  16. Point(Circle[E, Sisi]) → F
  17. Segment(G, F) → a
  18. Point(Circle[A_1, 2]) → B_1
  19. Segment(F, E) → a_8
  20. Segment(B, F) → a_9
  21. Polygon(A, B, C, D) → poly1, a_{10}, b, c, d
  22. Polygon(E, F, G, H) → poly2, e, f, g, h
  23. Polygon(D, C, G, H) → poly3, d_1, c_1, g_1, h_1
  24. Polygon(A, B, F, E) → poly4, a_{11}, b_1, f_1, e_1
  25. Polygon(B, C, G, F) → poly5, b_2, c_2, g_2, f_2
  26. Polygon(A, D, H, E) → poly6, a_{12}, d_2, h_2, e_2

AI Drawing Prompt Reference

Draw a cube with 8 vertices A to H and 4 faces poly1 to poly4. Start by creating point A, then draw a circle with A as the center and side length Sisi to get points B, E, D, H, C, G, and F. Next, connect these points to form edges a to a_9, and then use these edges and points to construct the four faces poly1 to poly4.
The prompt above was compiled from the original drawing commands and is for reference only.