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Volume of Revolution Between Two Curves

Volume of Revolution Between Two Curves
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2018-01-26 08:57
Solid GeometryCalculusIntegral
This example demonstrates the volume of a solid of revolution formed by two curves around an axis. Key mathematical concepts include integration and solid geometry. Using GeoGebra commands such as IntegralBetween, Surface, and Integral, the volume of the solid can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Textfield(f) → inputBox1
  2. Textfield(upperlimit) → inputBox2
  3. Textfield(lowerlimit) → inputBox3
  4. IntegralBetween(f, g, ll, ul) → h_1
  5. Textfield(g) → InputBox1
  6. IntegralBetween(f, g, ll, ul) → AreabyDefiniteIntegral
  7. Surface(u, (f(u) * cos(v)), (f(u) * sin(v)), u, ll, ul, v, 0, θ) → CurvedSurfacef
  8. Surface(u, (g(u) * cos(v)), (g(u) * sin(v)), u, ll, ul, v, 0, θ) → CurvedSurfaceg
  9. Surface(u, f(u) + (v * (g(u) - f(u))), 0, u, ll, ul, v, 0, 1) → Facexy
  10. Surface(u, ((f(u) + (v * (g(u) - f(u)))) * cos(θ)), ((f(u) + (v * (g(u) - f(u)))) * sin(θ)), u, ll, ul, v, 0, 1) → Facerotate
  11. Surface(ll, (u * cos(v)), (u * sin(v)), u, Min[f(ll), g(ll)], Max[f(ll), g(ll)], v, 0, θ) → LLface
  12. Surface(ul, (u * cos(v)), (u * sin(v)), u, Min[f(ul), g(ul)], Max[f(ul), g(ul)], v, 0, θ) → ULface
  13. Integral(f, ll, ul) → intf
  14. Integral(g, ll, ul) → intg
  15. Surface(u, ((v * f(u)) * cos(θ)), ((v * f(u)) * sin(θ)), u, ll, ul, v, 0, 1) → Facerotatef
  16. Surface(u, ((v * g(u)) * cos(θ)), ((v * g(u)) * sin(θ)), u, ll, ul, v, 0, 1) → Facerotateg
  17. Surface(u, (v * f(u)), 0, u, ll, ul, v, 0, 1) → Facexyf
  18. Surface(u, (v * g(u)), 0, u, ll, ul, v, 0, 1) → Facexyg
  19. Surface(ll, (u * cos(v)), (u * sin(v)), u, 0, f(ll), v, 0, θ) → LLfacef
  20. Surface(ll, (u * cos(v)), (u * sin(v)), u, 0, g(ll), v, 0, θ) → LLfaceg
  21. Surface(ul, (u * cos(v)), (u * sin(v)), u, 0, f(ul), v, 0, θ) → ULfacef
  22. Surface(ul, (u * cos(v)), (u * sin(v)), u, 0, g(ul), v, 0, θ) → ULfaceg
  23. Integral(f, ll, ul) → AreabyDefiniteIntegralf
  24. Integral(g, ll, ul) → AreabyDefiniteIntegralg