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Volumes of Similar Polyhedra

Volumes of Similar Polyhedra
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2016-03-03 00:02
Solid GeometryGeometric Construction
This example demonstrates the volume relationships of similar polyhedra. Key mathematical concepts include the properties of similar polyhedra and volume calculations. Using GeoGebra commands such as Circle, Rotate, Segment, Polygon, Prism, and Volume, similar polyhedra can be constructed and their volumes calculated. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Circle(A, B, xOyPlane) → c
  2. Rotate(B, 33, A) → B'
  3. Rotate(B', 2, A) → B''
  4. Rotate(B'', 1, A) → B'''
  5. Segment(B, B') → a
  6. Segment(B', B'') → b
  7. Segment(B'', B''') → d
  8. Segment(B''', B) → e
  9. Radius(c) → g
  10. Circle(C, (f * g)) → h_1
  11. Point(h_1) → D
  12. Rotate(D, 33, C) → D'
  13. Rotate(D', 2, C) → D''
  14. Rotate(D'', 1, C) → D'''
  15. Segment(D, D') → i
  16. Segment(D', D'') → j
  17. Segment(D'', D''') → k
  18. Segment(D''', D) → l
  19. Angle(B'', B', B) → α
  20. Angle(B, B''', B'') → β
  21. Angle(B''', B'', B') → γ
  22. Angle(B', B, B''') → δ
  23. Angle(D'', D', D) → ε
  24. Angle(D', D, D''') → ζ
  25. Angle(D, D''', D'') → η
  26. Angle(D''', D'', D') → θ
  27. Polygon(B', B, B''', B'') → poly1, b', b_1, b''', b''
  28. Polygon(D', D, D''', D'') → poly2, d', d_1, d''', d''
  29. Area(poly1) → Area_1
  30. Area(poly2) → Area_2
  31. Perimeter(poly1) → Perimeter_1
  32. Perimeter(poly2) → Perimeter_2
  33. Prism(poly1, h) → prism_1, E, edgeB'E, edgeBF, edgeB'''G, edgeB''H, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceBB'EF, faceBB'''GF, faceB''B'''GH, faceB'B''HE, faceEFGH
  34. Prism(poly2, (f * h)) → prism_2, I, edgeD'I, edgeDJ, edgeD'''K, edgeD''L, edgeIJ, edgeJK, edgeKL, edgeIL, J, K, L, faceDD'IJ, faceDD'''KJ, faceD''D'''KL, faceD'D''LI, faceIJKL
  35. Volume(prism_1) → Vol_1
  36. Volume(prism_2) → Vol_2