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Disk Method for Volume of Revolution

Disk Method for Volume of Revolution
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2016-11-11 05:10
FunctionCalculusIntegral
In collections Volume Apps
This example demonstrates the disk method for calculating the volume of a solid of revolution. Key mathematical concepts include integration and the calculation of the volume of a solid of revolution. Using GeoGebra commands such as CurveCartesian and Surface, the cross-sectional disks of the solid are constructed, and their volumes are calculated. Suitable for high school mathematics education and students learning calculus.

GeoGebra Commands & Parameters

  1. Textfield(f) → Function
  2. Textfield(a) → Textfeld2
  3. Textfield(b) → Textfeld3
  4. CurveCartesian(t, (f(t) * cos(φ)), (f(t) * sin(φ)), t, a, b) → k_x
  5. Ray((0, c), Vector[(1, 0)]) → g_1
  6. Intersect(f, g_1, (1, f(1))) → I
  7. Ray((0, d), Vector[(1, 0)]) → g_2
  8. Intersect(f, g_2, (d, f(d))) → J
  9. CurveCartesian((t * cos(ϕ)), f(t), (t * sin(ϕ)), t, x(I), x(J)) → k_y
  10. CurveCartesian(t, f(t), 0, t, -5, 5) → k
  11. Textfield(c) → Textfeld4
  12. Textfield(d) → Textfeld5
  13. Segment(A, G) → s_1
  14. Segment(B, F) → s_2
  15. Surface(u, (f(u) * cos(w)), (f(u) * sin(w)), u, a, b, w, 0, φ) → f_x
  16. Surface((uu * cos(ww)), f(uu), (uu * sin(ww)), uu, x(I), x(J), ww, 0, ϕ) → f_y
  17. Invert(f) → f_u
  18. Segment(C, I) → s_3
  19. Segment(D, J) → s_4
  20. CurveCartesian(x(B), t, t, y(B), f(x(B))) → LineCapRight
  21. CurveCartesian(x(A), t, t, y(A), f(x(A))) → LineCapLeft
  22. Surface(x(A), y(A) + ((s * (f(x(A)) - y(A))) * cos(t)), ((s * (f(x(A)) - y(A))) * sin(t)), s, 0, 1, t, 0, φ) → CapLeft
  23. Surface(x(B), y(B) + ((s * (f(x(B)) - y(B))) * cos(t)), ((s * (f(x(B)) - y(B))) * sin(t)), s, 0, 1, t, 0, φ) → CapRight
  24. CurveCartesian(t, y(C), t, x(C), f_u(y(C))) → LineCapBottom
  25. CurveCartesian(t, y(D), t, x(D), f_u(y(D))) → LineCapTop