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Solid of Revolution by Andreas Lindner

Solid of Revolution by Andreas Lindner
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2014-11-14 14:46
Solid GeometryCalculusIntegral
In collections Selected Examples Volume of Revolution Volumes of Solids
This example demonstrates the generation of a solid through rotation of a graph around the x- or y-axis. Key mathematical concepts include integral calculus and solid geometry. It utilizes various GeoGebra commands such as curve drawing, rotation, and surface generation. 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

AI Drawing Prompt Reference

Draw a solid of revolution by rotating a function graph around the x-axis or y-axis. First, draw a horizontal line and find its intersections with the function. Then plot the function curve and set the rotation angle. Generate the surface of the solid based on the function's range and consider different rotation directions. Finally, connect key points to form segments, showcasing the structure of the solid.
The prompt above was compiled from the original drawing commands and is for reference only.