MathPlotAI Logo MathPlotAI

Cube and Cuboid Volume Calculation

Cube and Cuboid Volume Calculation
Loading the math board and drawing, please wait…
2016-06-21 09:05
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the comparison and relationship between the volume calculations of a cube and a cuboid. It involves core mathematical concepts such as volume formulas, arithmetic mean, continuity, triangles, multiplication, and probability. The construction uses GeoGebra commands and objects like Point, Segment, Polygon, Intersect, Rotate, Vector, Translate, and Textfield. It is suitable for high school students learning and understanding solid geometry volume calculations and related mathematical concepts.

GeoGebra Commands & Parameters

  1. Point(Circle[A, r]) → B
  2. Segment(A, B) → f
  3. Point(Circle[B, r]) → C
  4. Segment(B, C) → g
  5. Point(Circle[C, r]) → D
  6. Segment(C, D) → h
  7. Polygon(D, A, B, C) → poly1, d, a, b, c
  8. Segment(D, B) → i
  9. Segment(A, C) → j
  10. Intersect(j, i) → E
  11. Rotate(D, (-rot), E) → D'
  12. Rotate(A, (-rot), E) → A'
  13. Rotate(B, (-rot), E) → B'
  14. Rotate(C, (-rot), E) → C'
  15. Polygon(D', A', B', C') → poly1', d', a', b', c'
  16. Point(Circle[F, r]) → G
  17. Segment(F, G) → k
  18. Point(Circle[G, r]) → H
  19. Segment(G, H) → m
  20. Point(Circle[H, r]) → I
  21. Segment(H, I) → n
  22. Segment(I, G) → q
  23. Segment(F, H) → s
  24. Intersect(s, q) → J
  25. Point(Circle[A', r]) → K
  26. Segment(A', K) → t
  27. Point(Circle[D', r]) → L
  28. Segment(D', L) → e
  29. Point(Circle[C', r]) → M
  30. Segment(C', M) → f_1
  31. Point(Circle[B', r]) → N
  32. Segment(B', N) → g_1
  33. Polygon(K, N, M, L) → poly2, k_1, n_1, m_1, l_1
  34. Point(Circle[O, airk]) → P
  35. Segment(O, P) → h_1
  36. Vector(P, O) → u
  37. Translate(N, u) → N'
  38. Translate(M, u) → M'
  39. Translate(L, u) → L'
  40. Translate(K, u) → K'
  41. Translate(O, Vector[(0, 0)]) → O'
  42. Translate(P, Vector[(0, 0)]) → P'
  43. Segment(O', P') → i_1
  44. Polygon(N', B', C', M') → poly3, n', b'_1, c'_1, m'
  45. Polygon(M', L', D', C') → poly4, m'_1, l', d'_1, c'_2
  46. Polygon(K', L', D', A') → poly5, k', l'_1, d'_2, a'_1
  47. Polygon(K', N', B', A') → poly6, k'_1, n'_1, b'_2, a'_2
  48. Polygon(N', K', L', M') → poly7, n'_2, k'_2, l'_2, m'_2
  49. Point(Circle[Q, p]) → R
  50. Segment(Q, R) → j_1
  51. Point(Circle[R, l]) → S
  52. Segment(R, S) → p_1
  53. Point(Circle[S, p]) → U
  54. Segment(S, U) → r_1
  55. Polygon(U, Q, R, S) → poly8, u_1, q_1, r_2, s_1
  56. Segment(U, R) → t_1
  57. Segment(S, Q) → a_1
  58. Intersect(a_1, t_1) → T
  59. Rotate(U, (-rot), T) → U'
  60. Rotate(Q, (-rot), T) → Q'
  61. Rotate(R, (-rot), T) → R'
  62. Rotate(S, (-rot), T) → S'
  63. Polygon(U', Q', R', S') → poly8', u', q', r', s'
  64. Point(Circle[Q', ti]) → V
  65. Segment(Q', V) → b_1
  66. Point(Circle[S', ti]) → W
  67. Segment(S', W) → c_1
  68. Point(Circle[U', ti]) → Z
  69. Segment(U', Z) → d_1
  70. Point(Circle[R', ti]) → A_1
  71. Segment(R', A_1) → e_1
  72. Polygon(Z, V, A_1, W) → poly9, z_1, v, a_2, w
  73. Point(Circle[B_1, tbair]) → C_1
  74. Segment(B_1, C_1) → f_2
  75. Vector(B_1, C_1) → v_1
  76. Translate(S', v_1) → S''
  77. Translate(U', v_1) → U''
  78. Translate(Q', v_1) → Q''
  79. Translate(R', v_1) → R''
  80. Polygon(R', R'', S'', S') → poly10, r'_1, r'', s'', s'_1
  81. Polygon(S'', U'', U', S') → poly11, s''_1, u'', u'_1, s'_2
  82. Polygon(R'', Q'', Q', R') → poly12, r''_1, q'', q'_1, r'_2
  83. Polygon(Q'', U'', U', Q') → poly13, q''_1, u''_1, u'_2, q'_2
  84. Polygon(Q'', R'', S'', U'') → poly14, q''_2, r''_2, s''_2, u''_2
  85. Textfield(p) → InputBox1
  86. Textfield(l) → InputBox2
  87. Textfield(ti) → InputBox3
  88. Textfield(r) → InputBox4