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Volume of a Solid of Revolution: Washer Method

Volume of a Solid of Revolution: Washer Method
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2017-01-19 01:02
Solid GeometryCalculusIntegral
In collections BC Calculus
This example demonstrates the calculation of the volume of a solid of revolution, particularly using the washer method. It involves core calculus concepts such as the volume of a solid of revolution and the washer method. Using GeoGebra commands like Dilate, Segment, Cylinder, Circle, etc., users can dynamically modify parameters to observe volume changes. Suitable for high school and above students learning calculus.

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'