Revolution Volume Integration Demo

Revolution Volume Integration Demo
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2020-04-02 00:39
① This example dynamically displays a solid of revolution formed by rotating a plane curve around an axis, and visually demonstrates the volume calculation via integration. ② Core mathematical concept: definite integral applied to volumes of revolution (disk/washer or shell method), involving integration variables, bounds, and accumulation of volume elements. ③ Construction: uses GeoGebra commands CurveCartesian to define the generating curve and Surface to create the rotated surface; sliders control rotation angle or curve parameters to animate the volume; objects a–n likely include curve equations, axis, integration interval, and computed volume values. ④ Suitable for high school advanced or college calculus courses, for classroom demonstrations or student exploration of volume by integration.

GeoGebra Commands & Parameters

  1. CurveCartesian(t, t^(2) / 5, 0, t, 2, 4) → a
  2. Surface(a, (2 * π), xAxis) → b
  3. CurveCartesian(t, t^(2) / 5, 0, t, 0, 6) → c
  4. CurveCartesian(t, t^(2) / 5, 0, t, 2, 2.01) → d
  5. Surface(d, (2 * π), xAxis) → e
  6. CurveCartesian(t, t^(2) / 5, 0, t, 3.99, 4) → f
  7. Surface(a, (2 * π), yAxis) → h
  8. Surface(f, (2 * π), xAxis) → g
  9. CurveCartesian(t, t^(2) / 5, 0, t, 3, 3.1) → i
  10. Surface(i, (2 * π), xAxis) → j
  11. CurveCartesian(3, t^(2) / 5, 0, t, 0, 3) → k
  12. Surface(k, (2 * π), xAxis) → l
  13. CurveCartesian(3.1, t^(2) / 5, 0, t, 0, 3.1) → m
  14. Surface(m, (2 * π), xAxis) → n