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Volumes of Revolution, Washers

Volumes of Revolution, Washers
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2019-04-17 04:45
Solid GeometryCalculusDerivative
This example demonstrates the generation of solid volumes through rotating regions of curves, and illustrates the washer method for volume calculation. Key math concepts include solid of revolution, derivatives, integration, limits, and geometric construction. It utilizes GeoGebra commands/objects like Intersect, Segment, Circle, Textfield, CurveCartesian, and Surface as outlined in the construction summary. Suitable for high school and above students learning volume calculation in calculus, and for geometric visualization purposes.

GeoGebra Commands & Parameters

  1. Intersect(f, i, (-0.5, 4.246657213746546)) → A
  2. Intersect(i, xAxis) → B
  3. Segment(A, B) → j
  4. Segment(A, B) → l
  5. Circle(xAxis, A) → c
  6. Textfield(f) → InputBox1
  7. CurveCartesian(t, f(t), t, a, b) → d
  8. Surface(d, p, m) → e
  9. Intersect(g, i, (-0.5, 1.1666666666666667)) → C
  10. Segment(A, C) → n
  11. Circle(xAxis, C) → q
  12. CurveCartesian(t, g(t), t, a, b) → o
  13. Surface(o, p, m) → s
  14. Textfield(g) → InputBox2
  15. CurveCartesian(a, (t * f(a)) + ((1 - t) * g(a)), t, 0, 1) → t
  16. Surface(t, p, m) → u
  17. CurveCartesian(b, (t * f(b)) + ((1 - t) * g(b)), t, 0, 1) → v
  18. Surface(v, p, m) → w