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Washer Volume Visualization

Washer Volume Visualization
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2020-04-22 02:54
Solid GeometryCalculusOptimizationGraphing
In collections Calculus - Applications of Integrals - Areas and Volumes
This example dynamically demonstrates the volume of solids of revolution using the washer method, covering core calculus concepts like integration and optimization. It employs GeoGebra commands such as Dilate, Segment, Cylinder, Circle, Vector, Translate, and Rotate for construction, making it ideal for high school and introductory calculus students learning volume calculations.

GeoGebra Commands & Parameters

  1. Dilate(B, If[0 < j ≤ 1, 1 - j, 0], A) → B'
  2. Segment(B, B') → l
  3. Cylinder(B, B', r) → a, c, d, b
  4. Dilate(E, If[2 < j ≤ 3, 3 - j, 0], C) → E'
  5. Segment(E, E') → f
  6. Dilate(G, If[1 < j ≤ 2, 2 - j, 0], C) → G'
  7. Dilate(F, If[1 < j ≤ 2, 2 - j, 0], E) → F'
  8. Segment(G, G') → g
  9. Segment(F, F') → i
  10. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], H) → A'
  11. Dilate(A, If[3 < j ≤ 4, 4 - j, 0], D) → A'_1
  12. Circle(A', A'_1, I) → k
  13. Dilate(A, If[4 < j ≤ 5, 5 - j, 0], B) → A'_2
  14. Cylinder(A, A'_2, e) → m, p, q, n
  15. Dilate(G, If[1 < j ≤ 2, 2 - j, 0], A) → A'_3
  16. Segment(G, A'_3) → s
  17. Dilate(A, If[6 < j ≤ 7, 7 - j, 0], B) → A'_4
  18. Vector(A, A'_4) → u
  19. Translate(m, u) → m'
  20. Cylinder(A, A'_4, e) → o, t, c_1, v
  21. Dilate(B, If[7 < j ≤ 8, 8 - j, 0], J) → B'_1
  22. Vector(B, B'_1) → w
  23. Translate(m', w) → m''
  24. Dilate(J, If[8 < j ≤ 9, 9 - j, 0], K) → J'
  25. Segment(J, J') → f_1
  26. Dilate(C, If[9 < j ≤ 10, 10 - j, 0], L) → C'
  27. Vector(C, C') → u_1
  28. Translate(E, u_1) → E'_1
  29. Translate(E', u_1) → E''
  30. Segment(E'_1, E'') → f'
  31. Translate(G, u_1) → G'_1
  32. Translate(G', u_1) → G''
  33. Segment(G'_1, G'') → g'
  34. Translate(F, u_1) → F'_1
  35. Translate(F', u_1) → F''
  36. Segment(F'_1, F'') → i'
  37. Dilate(K, If[9 < j ≤ 10, 10 - j, 0], M) → K'
  38. Dilate(O, If[9 < j ≤ 10, 10 - j, 0], N) → O'
  39. Segment(K, K') → g_1
  40. Segment(O, O') → h_1
  41. Rotate(J, π, Line[(0, 0, 0), (0, 0, 1)]) → J'_1
  42. Rotate(J', π, Line[(0, 0, 0), (0, 0, 1)]) → J''
  43. Segment(J'_1, J'') → i_1
  44. Rotate(G, π, Line[(0, 0, 0), (0, 0, 1)]) → G'_2
  45. Rotate(A'_3, π, Line[(0, 0, 0), (0, 0, 1)]) → P
  46. Segment(G'_2, P) → s'