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3D Shape from Rotating a Rectangle Around the Y-Axis

3D Shape from Rotating a Rectangle Around the Y-Axis
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2016-01-28 02:51
TrigonometryCoordinate GeometrySolid GeometryCalculusGeometric Construction
In collections Shape Rotations Shape Rotations Shape Rotations
This example demonstrates the 3D shape created by rotating a rectangle around the y-axis. It involves core math concepts like solid geometry, rotation solids, and coordinate geometry. The construction uses GeoGebra commands/objects such as OrthogonalLine, Point, Intersect, Polygon, Segment, Cylinder, and Rotate. Suitable for high school students and above exploring spatial geometry and the formation of rotational solids.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, xAxis) → a
  2. OrthogonalLine(A, a) → b
  3. Point(b) → B
  4. Point(a) → C
  5. OrthogonalLine(C, a) → c
  6. OrthogonalLine(B, b) → d
  7. Intersect(c, d) → D
  8. Polygon(A, C, D, B) → poly1, a_1, c_1, d_1, b_1
  9. Intersect(a, xAxis) → E
  10. Intersect(d, xAxis) → F
  11. Segment(A, E) → e
  12. Cylinder(E, F, e) → f, g, h, i
  13. Cylinder(E, F, e + a_1) → j, k, p, l
  14. Segment(D, F) → m
  15. Segment(C, E) → n
  16. Rotate(D, r, xAxis) → D'
  17. Rotate(B, r, xAxis) → B'
  18. Segment(D', B') → q
  19. Rotate(B, r, xAxis) → B'_1
  20. Rotate(A, r, xAxis) → A'
  21. Segment(B'_1, A') → s
  22. Rotate(C, r, xAxis) → C'
  23. Rotate(D, r, xAxis) → D'_1
  24. Segment(C', D'_1) → t
  25. Rotate(A, r, xAxis) → A'_1
  26. Rotate(C, r, xAxis) → C'_1
  27. Segment(A'_1, C'_1) → e_1
  28. Rotate(B, (-r), xAxis) → B'_2