Volume Calculation and Rotation Solid Demo

GeoGebra Commands & Parameters

1. Line(A, xAxis) → a
2. OrthogonalLine(A, a) → q_4
3. Circle(A, 2) → r
4. Intersect(r, q_4, 2) → E
5. Intersect(r, a, 2) → B
6. OrthogonalLine(E, q_4) → s
7. OrthogonalLine(B, a) → t
8. Intersect(s, t) → F
9. Rotate(F, 45*°, E) → S'
10. Angle(F, E, S') → α
11. Segment(E, S') → i_1
12. Segment(E, F) → j_1
13. Midpoint(j_1) → T
14. Circle(E, T) → k_1
15. Intersect(k_1, i_1, 1) → H
16. Segment(E, H) → p_1
17. Line(H, j_1) → q_1
18. Line(F, p_1) → r_1
19. Intersect(q_1, r_1) → V
20. Segment(A, E) → s_1
21. Segment(F, B) → t_1
22. Line(B, r_1) → a_2
23. Line(V, s_1) → b_2
24. Intersect(a_2, b_2) → W
25. Polygon(A, B, F, E) → poly1, p_2, r_2, s_2, q_2
26. Polygon(B, W, V, F) → poly2, r_3, w, v, s_3
27. Polygon(E, F, V, H) → poly3, q_3, s_4, v_1, u
28. Translate(A, B - A) → A'
29. Translate(E, B - A) → E'
30. Sequence(Sequence[Polygon[Translate[A, Vector[k * Vector[A, B] + l * Vector[A, E]]], Translate[B, Vector[k * Vector[A, B] + l * Vector[A, E]]], Translate[F, Vector[k * Vector[A, B] + l * Vector[A, E]]], Translate[E, Vector[k * Vector[A, B] + l * Vector[E, A]]]], k, 0, o], l, 0, 0) → ligne
31. Sequence(Sequence[Polygon[Translate[E, Vector[l * Vector[A, B] + m * Vector[E, H]]], Translate[F, Vector[l * Vector[A, B] + m * Vector[E, H]]], Translate[V, Vector[l * Vector[A, B] + m * Vector[E, H]]], Translate[H, Vector[l * Vector[A, B] + m * Vector[E, H]]]], l, 0, o], m, 0, q) → liste3
32. Sequence(Polygon[Translate[B, k * (W - B) + o * (B - A)], Translate[W, k * (W - B) + o * (B - A)], Translate[V, k * (W - B) + o * (B - A)], Translate[F, k * (W - B) + o * (B - A)]], k, 0, q) → ligne2
33. Sequence(Sequence[Polygon[Translate[A, Vector[k * Vector[B, A] - l * Vector[E, A]]], Translate[B, Vector[k * Vector[B, A] - l * Vector[E, A]]], Translate[F, Vector[k * Vector[B, A] - l * Vector[E, A]]], Translate[E, Vector[k * Vector[B, A] - l * Vector[E, A]]]], k, 0, 0], l, 0, p) → liste
34. Sequence(Sequence[Polygon[Translate[B, Vector[-l * Vector[E, A] + m * Vector[E, H]]], Translate[W, Vector[-l * Vector[E, A] + m * Vector[E, H]]], Translate[V, Vector[-l * Vector[E, A] + m * Vector[E, H]]], Translate[F, Vector[-l * Vector[E, A] + m * Vector[E, H]]]], l, 0, p], m, 0, 0) → liste2
35. Translate(E, p * (E - A)) → E'_1
36. Translate(F, p * (E - A)) → F'
37. Translate(V, p * (E - A)) → V'
38. Translate(H, p * (E - A)) → H'
39. Polygon(E'_1, F', V', H') → Haut, e'_1, f', v', h'
40. Translate(A, (o + 1) * (B - A)) → Sommet1
41. Translate(A, (p + 1) * (E - A)) → Sommet2
42. OrthogonalLine(E'_1, s_1) → b
43. OrthogonalLine(Sommet1, p_2) → c
44. Intersect(b, c) → Sommet3
45. Translate(A, (q + 1) * (H - E)) → Sommet4
46. OrthogonalLine(Sommet4, p_2) → d
47. Segment(A, Sommet4) → e
48. Segment(A, E'_1) → f
49. Line(E'_1, e) → g
50. Intersect(d, g) → C
51. Line(Sommet3, g) → h
52. Line(C, b) → i
53. Intersect(h, i) → D
54. Line(D, d) → j
55. Line(Sommet1, h) → k
56. Intersect(j, k) → G
57. Segment(E'_1, Sommet3) → l
58. Segment(Sommet3, Sommet1) → m
59. Segment(Sommet3, D) → n
60. Segment(D, G) → a_1
61. Segment(D, C) → b_1
62. Segment(C, E'_1) → c_1
63. Segment(F', B) → d_1
64. Segment(V', V) → e_1
65. Segment(H', V') → f_1
66. Segment(A, Sommet1) → g_1
67. Point(g_1) → I
68. Segment(I, G) → h_1
69. Segment(F, E) → l_1
70. Segment(F, B) → m_1
71. Line(E, g_1) → n_1
72. Intersect(n_1, m) → J
73. Segment(F, J) → c_2
74. Segment(F', V') → d_2
75. Segment(B, W) → e_2
76. Line(J, h_1) → f_2
77. Intersect(a_1, f_2) → K
78. Point(h_1) → L
79. Segment(L, K) → g_2
80. Segment(J, K) → h_2
81. Line(H, h_1) → i_2
82. Line(K, l) → j_2
83. Intersect(i_2, j_2) → M
84. Segment(M, K) → k_2
85. Intersect(i_2, e_1) → N
86. Segment(N, M) → l_2
87. Intersect(r_1, j_2) → O
88. Segment(F, O) → m_2
89. Sequence(Segment[Translate[F, -k * (A - B)], Translate[O, -k * (A - B)]], k, 0, o) → seg4
90. Line(N, b_1) → n_2
91. Intersect(n_2, h_2) → P
92. Segment(N, P) → t_2
93. Line(V, t_2) → a_3
94. Intersect(a_3, h_2) → Q
95. Line(S', a_3) → b_3
96. Intersect(b_3, h_2) → R
97. Segment(V, Q) → c_3
98. Polygon(F, V, N, M, K, J) → poly4, f_3, v_2, n_3, m_3, k_3, j_3
99. Polygon(V, F, F', V') → poly5, v_3, f_4, f'_1, v'_1
100. Segment(N, M) → d_3
101. Segment(M, K) → e_3
102. Sequence(Segment[Translate[F, -k * (A - E)], Translate[E, -k * (A - E)]], k, 0, p) → seg_1
103. Sequence(Segment[Translate[F, k * (B - A)], Translate[B, k * (B - A)]], k, 0, o) → seg_2
104. Sequence(Segment[Translate[F, -l * (E - H) + o * (B - A)], Translate[B, -l * (E - H) + o * (B - A)]], l, 1, q) → seg10
105. Sequence(Segment[Translate[N, l * (H - E)], Translate[P, l * (H - E)]], l, -2, q - 3) → seg5
106. Sequence(Segment[Translate[B, -k * (B - F)], Translate[W, -k * (B - F)]], k, 1, p) → seg_3