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Volume of Revolution by Lam Meng Hwee

Volume of Revolution by Lam Meng Hwee
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2019-08-30 07:51
Solid GeometryCalculusIntegral
This example demonstrates how to generate a solid of revolution by rotating a plane figure and calculating its volume. Key mathematical concepts include integration and solid geometry. Using GeoGebra commands such as Point, CurveCartesian, Integral, etc., the solid of revolution can be constructed. Suitable for high school and above students learning calculus and solid geometry.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Point(xAxis) → A
  3. CurveCartesian(u, f(u), u, x(A), x(B)) → b
  4. Textfield(f) → InputBox1
  5. Integral(f, x(A), x(B)) → a
  6. CurveCartesian(x(A), t, t, 0, f(x(A))) → d
  7. CurveCartesian(x(B), t, t, 0, f(x(B))) → g
  8. Segment(C, C') → k
  9. Segment(D, D') → l
  10. Polygon(D', C', C, D) → q1, d', c', c_1, d_1
  11. Surface(b, (θ / 180 * π), i) → m
  12. CurveCartesian(t, y(C), t, 0, x(C)) → n
  13. Surface(n, (θ / 180 * π), yAxis) → p
  14. CurveCartesian(t, y(D), t, 0, x(D)) → o
  15. Surface(o, (θ / 180 * π), yAxis) → q
  16. Surface(b, (θ / 180 * π), j) → c
  17. Surface(d, (θ / 180 * π), j) → h
  18. Surface(g, (θ / 180 * π), j) → e