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Volume Calculation of Rotated Solids

Volume Calculation of Rotated Solids
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2018-04-21 08:50
Solid GeometryCalculusGraphing
This example demonstrates how to calculate the volume of a solid of revolution by rotating a plane figure. Key mathematical concepts include integration and solid geometry. Using GeoGebra commands such as Surface, Rotate, and If, the construction of the solid and its volume calculation are illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Textfield(f) → Textfeld1
  2. Textfield(a) → Textfeld2
  3. Textfield(b) → Textfeld3
  4. Line((0, c), Vector[(1, 0)]) → g_1
  5. Intersect(f, g_1, (1, f(1))) → I
  6. Line((0, d), Vector[(1, 0)]) → g_2
  7. Intersect(f, g_2, (d, f(d))) → J
  8. CurveCartesian(t, f(t), 0, t, -5, 5) → k
  9. Textfield(c) → Textfeld4
  10. Textfield(d) → Textfeld5
  11. Segment(A, G) → s_1
  12. Segment(B, F) → s_2
  13. Surface(u, (f(u) * cos(w)), (f(u) * sin(w)), u, a, b, w, 0, φ) → f_x
  14. Invert(f) → f_u
  15. Segment(C, I) → s_3
  16. Segment(D, J) → s_4
  17. Rotate(If[a ≤ x ≤ b, f(x)], φ, xAxis) → k_x
  18. If(f_u(c) < f_u(d), Rotate[If[f_u(c) ≤ x ≤ f_u(d), f], (-ϕ), yAxis], Rotate[If[f_u(d) ≤ x ≤ f_u(c), f], (-ϕ), yAxis]) → k_y
  19. If(f_u(c) < f_u(d), Surface[(uu * cos(ww)), f(uu), (uu * sin(ww)), uu, f_u(c), f_u(d), ww, 0, ϕ], Surface[(uu * cos(ww)), f(uu), (uu * sin(ww)), uu, f_u(d), f_u(c), ww, 0, ϕ]) → f_y