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Volume Element in Cylindrical Coordinates

Volume Element in Cylindrical Coordinates
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2019-09-01 10:52
TrigonometryCoordinate GeometrySolid GeometryCalculus
This example visualizes the volume element in cylindrical coordinates. It involves core math concepts like cylindrical coordinates, volume element, and integral calculus. Constructed using GeoGebra commands such as Line, Point, Intersect, Circle, Segment, CircleArc, and Cylinder. Suitable for university students in mathematics and physics learning multiple integrals and solid geometry.

GeoGebra Commands & Parameters

  1. Line((0.8, 0.6, 1), B) → c
  2. Point(c) → C
  3. Line(E, C) → h
  4. Intersect(h, eq2) → J, K
  5. Line(D, A) → g
  6. Intersect(g, eq2) → N, O
  7. Line((1, 0, 1), A) → d
  8. Circle(zAxis, C) → e
  9. Intersect(d, e) → F,
  10. Line(D, B) → f
  11. Line(D, G) → i
  12. Intersect(f, eq2) → L, M
  13. Segment(D, B) → k
  14. Segment(D, A) → j
  15. Segment(A, O) → n
  16. Segment(B, M) → p
  17. CircleArc(D, A, B) → s
  18. CircleArc(D, O, M) → t
  19. CircleArc(D, I, K) → d_1
  20. Segment(C, K) → q
  21. Segment(O, I) → f_1
  22. Segment(M, K) → h_1
  23. Segment(B, C) → g_1
  24. Segment(E, C) → m
  25. Segment(E, F) → l
  26. Segment(F, I) → r
  27. CircleArc(D, F, C) → c_1
  28. Segment(A, F) → e_1
  29. Circle(zAxis, (sqrt(2), 0, -1)) → k_1
  30. Cylinder(k_1, o) → u, r_1, v
  31. Circle(zAxis, (1, 0, -1)) → q_1
  32. Cylinder(q_1, w) → a_1, t_1, b_1