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Volume Enlargement Demonstration

Volume Enlargement Demonstration
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2011-11-12 21:25
Solid GeometryGeometric Construction
In collections Area, Surface Area, Volume--Nets
This example demonstrates the process of volume enlargement through transformation controls. Core mathematical concepts include solid geometry, similarity transformations, and volume calculations. Construction highlights the use of GeoGebra commands and objects such as Point, Segment, Polygon, Dilate, Ray, Line. Suitable for high school students learning solid geometry and transformations.

GeoGebra Commands & Parameters

  1. Point(Circle[A, height]) → B
  2. Segment(A, B) → a
  3. Point(Circle[A, depth]) → C
  4. Segment(A, C) → b
  5. Point(Circle[A, width]) → K
  6. Segment(A, K) → h
  7. Point(Circle[K, height]) → D
  8. Segment(K, D) → c
  9. Point(Circle[K, depth]) → E
  10. Segment(K, E) → d
  11. Segment(C, E) → e
  12. Point(Circle[E, height]) → F
  13. Segment(E, F) → f
  14. Segment(F, D) → g
  15. Segment(D, B) → i
  16. Polygon(A, K, D, B) → poly1, a_1, k, d_1, b_1
  17. Polygon(A, C, E, K) → poly2, a_2, c_1, e_1, k_1
  18. Polygon(E, F, D, K) → poly3, e_2, f_1, d_2, k_2
  19. Dilate(A, sf, centre) → A'
  20. Dilate(K, sf, centre) → K'
  21. Dilate(D, sf, centre) → D'
  22. Dilate(B, sf, centre) → B'
  23. Polygon(A', K', D', B') → poly1', a', k', d', b'
  24. Dilate(A, sf, centre) → A'_1
  25. Dilate(C, sf, centre) → C'
  26. Dilate(E, sf, centre) → E'
  27. Dilate(K, sf, centre) → K'_1
  28. Polygon(A'_1, C', E', K'_1) → poly2', a'_1, c', e', k'_1
  29. Dilate(E, sf, centre) → E'_1
  30. Dilate(F, sf, centre) → F'
  31. Dilate(D, sf, centre) → D'_1
  32. Dilate(K, sf, centre) → K'_2
  33. Polygon(E'_1, F', D'_1, K'_2) → poly3', e'_1, f', d'_1, k'_2
  34. Dilate(K, sf, centre) → K'_3
  35. Dilate(E, sf, centre) → E'_2
  36. Segment(K'_3, E'_2) → d'_2
  37. Ray(centre, C') → j
  38. Ray(centre, K') → l
  39. Ray(centre, B') → m
  40. Line(G, H) → p