MathPlotAI Logo MathPlotAI

Rotating a Cylinder

Rotating a Cylinder
Loading the math board and drawing, please wait…
2018-12-07 20:26
Solid GeometryParametric EquationGeometric ConstructionGraphing
This example demonstrates the process of generating a 3D cylinder by rotating a 2D curve. Key math concepts include solids of revolution, parametric equations, and 3D geometry. Construction highlights the use of GeoGebra commands/objects like Intersect, Point, Circle, Cylinder, Surface, CurveCartesian, and Translate. Suitable for high school and above students studying applications of 3D geometry and parametric equations.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xOyPlane) → A
  2. Point(zAxis) → B
  3. Circle(A, 3, zAxis) → c
  4. Cylinder(c, z(B)) → a, d, b
  5. Surface((u * cos(t)), (u * sin(t)), (z(B) * t / π), t, 0, π, u, -3, 3) → e
  6. CurveCartesian((3 * cos(t)), (3 * sin(t)), (z(B) * t / π), t, 0, π) → f
  7. CurveCartesian((3 * cos(t - π)), (3 * sin(t - π)), (z(B) * t / π), t, 0, π) → g
  8. Surface(f, π, zAxis) → h
  9. Surface(g, π, zAxis) → i
  10. CurveCartesian(t, 0, z(B), t, 0, 3) → k
  11. Surface(k, π, zAxis) → l
  12. CurveCartesian(t, 0, 0, t, -3, 0) → j
  13. Surface(j, π, zAxis) → m
  14. Translate(Rotate[l, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → o
  15. Translate(Rotate[i, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → p
  16. Translate(Rotate[m, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → q
  17. Translate(Rotate[e, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → r
  18. Translate(Rotate[f, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → s
  19. Translate(Rotate[g, n, zAxis], Vector[(0, 0, (z(B) * n / π))]) → t
  20. Surface(CurveCartesian[t, 0, z(B), t, -3, 0], π, zAxis) → u
  21. Surface(CurveCartesian[t, 0, 0, t, 0, 3], π, zAxis) → v