Surface Area and Volume Relationships

GeoGebra Commands & Parameters

1. Segment((0, 0), (0, 1)) → a
2. OrthogonalLine(A, a) → b
3. Point(b) → B
4. Segment(A, B) → c
5. Circle(C, c) → d
6. Point(d) → D
7. Segment(C, D) → e
8. Rotate(D, -90°, C) → D'
9. Angle(D', C, D) → α
10. OrthogonalLine(D, e) → f
11. OrthogonalLine(C, e) → g
12. OrthogonalLine(D', g) → h
13. Segment(C, D') → i
14. Intersect(h, f) → E
15. Segment(D', E) → j
16. Segment(D, E) → k
17. Circle(D', 36 / c^(2)) → p
18. Intersect(p, g) → G, H
19. Segment(D', G) → l
20. OrthogonalLine(G, g) → m
21. Intersect(m, f) → F
22. Segment(G, F) → n
23. Segment(F, E) → q
24. Circle(E, c) → r
25. OrthogonalLine(E, q) → s
26. Intersect(r, s) → I, J
27. Segment(E, I) → t
28. OrthogonalLine(I, s) → a_1
29. Intersect(m, a_1) → K
30. Segment(F, K) → b_1
31. Segment(I, K) → c_1
32. Circle(G, c) → d_1
33. Intersect(d_1, g) → L, M
34. OrthogonalLine(L, g) → e_1
35. Segment(G, L) → f_1
36. Intersect(e_1, f) → N
37. Segment(L, N) → g_1
38. Segment(N, F) → h_1
39. Circle(D', c) → k_1
40. OrthogonalLine(D', i) → i_1
41. Intersect(k_1, i_1) → O, P
42. OrthogonalLine(O, i_1) → j_1
43. OrthogonalLine(G, f_1) → l_1
44. Intersect(l_1, j_1) → Q
45. Polygon(O, D', G, Q) → poly1, o, d', g_2, q_1
46. Polygon(D', E, F, G) → poly2, d'_1, e_2, f_2, g_3
47. Polygon(C, D, E, D') → poly3, c_2, d_2, e_3, d'_2
48. Polygon(G, F, N, L) → poly4, g_4, f_3, n_1, l_2
49. Polygon(E, I, K, F) → poly5, e_4, i_2, k_2, f_4
50. Circle(D, 36 / c^(2)) → p_1
51. Intersect(p_1, f, 2) → R
52. OrthogonalLine(R, f) → m_1
53. Intersect(g, m_1) → S
54. Polygon(C, S, R, D) → poly6, c_3, s_1, r_1, d_3