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Cylinder Volume and Surface Area

Cylinder Volume and Surface Area
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2016-01-19 18:36
Coordinate GeometrySolid GeometryCalculusGeometric Construction
This example demonstrates the calculation of volume and surface area for a cylinder. Key math concepts include cylinder geometry, area and volume formulas, and analytical geometry. Construction highlights involve GeoGebra commands such as Midpoint, Circle, Segment, OrthogonalLine, Intersect, Point, Conic, Polygon, Vector, Translate, and Line to model the cylinder. Suitable for high school students and beginners needing basic solid geometry calculations.

GeoGebra Commands & Parameters

  1. Midpoint(M, N) → T
  2. Circle(T, h) → g1
  3. Segment(T, M) → m
  4. OrthogonalLine(T, m) → a1
  5. Intersect(g1, a1) → K, S
  6. Point(f) → Q
  7. Point(f) → P
  8. Point(i) → R
  9. Point(i) → O
  10. Point(i) → L
  11. Segment(S_1, T) → n
  12. Conic(R, L, O, P, Q) → c_1
  13. Conic(R, L, O, P, Q) → e1
  14. Polygon(S, N, M) → poly1, m_1, s_1, n_1
  15. Vector(T, S) → u
  16. Translate(i1, u) → h1
  17. Translate(e1, u) → p
  18. Translate(f1, u) → f2
  19. Translate(f1, u) → g2
  20. Translate(N, u) → H
  21. Translate(M, u) → I
  22. Segment(I, M) → a
  23. Segment(H, N) → b
  24. Circle(A, h / 2) → c
  25. Point(c) → B
  26. Line(A, B) → d
  27. OrthogonalLine(B, d) → j
  28. Intersect(c, d) → C, D
  29. Line(D, j) → k
  30. Circle(B, (3.141592653589793 * r)) → q
  31. Intersect(q, j) → E, F
  32. Circle(D, (3.141592653589793 * r)) → s
  33. Intersect(s, k) → G, J
  34. Polygon(F, E, G, J) → poly2, f_1, e_1, g_1, j_1
  35. Circle(B, r) → t
  36. Intersect(t, d) → U, V
  37. Circle(V, B) → c1
  38. Circle(D, r) → d1
  39. Intersect(d1, d) → W, Z
  40. Circle(W, D) → k1
  41. Circle(V, B) → p1
  42. Circle(W, D) → q1
  43. Polygon(F, E, G, J) → poly3, f_2, e_2, g_2, j_2
  44. Midpoint(j_2) → A1
  45. Midpoint(e_2) → B1
  46. Midpoint(F, A1) → C1
  47. Midpoint(C1, F) → D1
  48. Midpoint(E, B1) → E1
  49. Midpoint(E, E1) → F1
  50. Midpoint(D1, F1) → G1
  51. Midpoint(F, B) → H1
  52. Midpoint(F, H1) → I1
  53. Midpoint(J, D) → J1
  54. Midpoint(J, J1) → K1
  55. Midpoint(I1, K1) → L1
  56. Vector(G1, F1) → v
  57. Vector(G1, D1) → w
  58. Vector(L1, I1) → z
  59. Vector(L1, K1) → l
  60. Point(p1) → M1
  61. Segment(M1, V) → b1
  62. Midpoint(b1) → N1