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Surface Area and Volume Elements in Spherical Coordinates

Surface Area and Volume Elements in Spherical Coordinates
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2019-09-01 18:06
Coordinate GeometrySolid GeometryCalculus
This example demonstrates surface area and volume elements in spherical coordinates. Key mathematical concepts include spherical coordinates, methods for calculating surface area and volume. Using GeoGebra commands such as Circle, Point, CircleArc, etc., it provides a visual understanding of these concepts. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Circle(zAxis, (1, 0, 0)) → p_1
  2. Point(p_1) → C
  3. CircleArc(A, C, B) → c
  4. Point(c) → E
  5. CircleArc(A, D, B) → d
  6. Circle(zAxis, E) → e
  7. Intersect(d, e) → F, G, ,
  8. Ray(A, C) → f
  9. Ray(A, D) → g
  10. Ray(A, E) → h
  11. Ray(A, G) → i
  12. Intersect(f, eq2) → H,
  13. Intersect(h, eq2) → I,
  14. Intersect(i, eq2) → J,
  15. Intersect(g, eq2) → K,
  16. CircleArc(A, C, E) → k
  17. CircleArc(A, D, G) → p
  18. CircleArc(A, H, I) → q
  19. CircleArc(A, K, J) → r
  20. CircleArc(A, C, D) → s
  21. CircleArc(A, E, G) → t
  22. CircleArc(A, I, J) → c_1
  23. CircleArc(A, H, K) → d_1
  24. Segment(C, H) → j
  25. Segment(D, K) → l
  26. Segment(E, I) → m
  27. Segment(G, J) → n
  28. Segment(A, E) → a
  29. Segment(A, G) → b
  30. Segment(A, D) → f_1
  31. Segment(A, C) → g_1
  32. Circle(zAxis, I) → e_1
  33. Center(e_1) → M
  34. Segment(M, I) → i_1
  35. Segment(A, M) → h_1
  36. Segment(A, I) → j_1
  37. Segment(A, J) → k_1
  38. Segment(A, H) → l_1
  39. Segment(A, K) → m_1