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Volumes of Cubes and Prisms by LearnZillion

Volumes of Cubes and Prisms by LearnZillion
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2018-04-17 19:34
Solid GeometryTransformation
This example demonstrates the calculation of volumes of cubes and prisms. Key mathematical concepts include geometric transformations, reflection, cuboid, linear functions, and congruence. Using GeoGebra commands such as Dilate (scaling), Polygon (polygon), Vector (vector), Sequence (sequence), and Translate (translation), the construction of cubes and prisms is achieved, and their volumes are calculated through transformations and computations. Suitable for middle and high school students studying solid geometry and volume calculations.

GeoGebra Commands & Parameters

  1. Dilate(E, a, A) → E'_1
  2. Dilate(F, a, D) → F'_1
  3. Dilate(G, a, C) → G'_1
  4. Dilate(A, b, D) → A'_1
  5. Dilate(E'_1, b, F'_1) → E''_1
  6. Dilate(B, b, C) → B'_1
  7. Dilate(F'_1, c, G'_1) → F''_1
  8. Dilate(D, a, B) → D'_1
  9. Dilate(E'_1, c, D'_1) → E''
  10. Dilate(E'', b, F''_1) → E'''
  11. Dilate(A'_1, c, B'_1) → A''_1
  12. Dilate(D, c, C) → D'_2
  13. Polygon(C, G'_1, F''_1, D'_2) → poly1, c_2, g', f'', d'
  14. Polygon(C, D'_2, A''_1, B'_1) → poly2, c_1, d'_1, a'', b'
  15. Polygon(A''_1, D'_2, F''_1, E''') → poly3, a''_1, d'_2, f''_1, e'''
  16. Polygon(B, A, D, C) → poly4, b_1, a_1, d_3, c_3
  17. Polygon(C, D, F, G) → poly5, c_4, d_1, f_2, g_1
  18. Polygon(D, F, E, A) → poly6, d_2, f_1, e_1, a_2
  19. Vector(C, D) → u
  20. Sequence(Segment[Translate[C, Vector[(j * u)]], Translate[G'_1, Vector[(j * u)]]], j, 1, c - 1) → list1
  21. Sequence(Segment[Translate[B'_1, Vector[(j * u)]], Translate[C, Vector[(j * u)]]], j, 1, c - 1) → list2
  22. Vector(C, G) → v
  23. Vector(C, B) → w
  24. Sequence(Segment[Translate[C, Vector[(j * v)]], Translate[D'_2, Vector[(j * v)]]], j, 1, a - 1) → list3
  25. Sequence(Segment[Translate[C, Vector[(j * w)]], Translate[D'_2, Vector[(j * w)]]], j, 1, b - 1) → list4
  26. Sequence(Segment[Translate[F''_1, Vector[(j * w)]], Translate[D'_2, Vector[(j * w)]]], j, 1, b - 1) → list5
  27. Sequence(Segment[Translate[D'_2, Vector[(j * v)]], Translate[A''_1, Vector[(j * v)]]], j, 1, a - 1) → list6
  28. Dilate(G, (a * d), C) → G'
  29. Dilate(F, (a * d), D) → F'
  30. Dilate(F', (c * f), G') → F''
  31. Dilate(D, (c * f), C) → D'
  32. Dilate(B, (b * e), C) → B'
  33. Dilate(A, (b * e), D) → A'
  34. Dilate(A', (c * f), B') → A''
  35. Vector(D', F'') → z
  36. Translate(A'', z) → A'''
  37. Polygon(D', C, G', F'') → poly7, d'_3, c_5, g'_1, f_4
  38. Polygon(D', C, B', A'') → poly8, d_6, c_6, b'_1, a_4
  39. Polygon(A'', D', F'', A''') → poly9, a''_3, d'_5, f''_3, a'''
  40. Sequence(Segment[Translate[C, Vector[((j * c) * u)]], Translate[G', Vector[((j * c) * u)]]], j, 1, f) → list7
  41. Sequence(Segment[Translate[C, Vector[((j * c) * u)]], Translate[B', Vector[((j * c) * u)]]], j, 1, f) → list8
  42. Sequence(Segment[Translate[D', Vector[((j * a) * v)]], Translate[C, Vector[((j * a) * v)]]], j, 1, d) → list9
  43. Sequence(Segment[Translate[D', Vector[((j * b) * w)]], Translate[C, Vector[((j * b) * w)]]], j, 1, e) → list10
  44. Sequence(Segment[Translate[A'', Vector[((j * a) * v)]], Translate[D', Vector[((j * a) * v)]]], j, 1, d) → list11
  45. Sequence(Segment[Translate[F'', Vector[((j * b) * w)]], Translate[D', Vector[((j * b) * w)]]], j, 1, e) → list12