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Solids of Revolution (Rectangle)

Solids of Revolution (Rectangle)
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2017-02-11 10:16
FunctionSolid GeometryCalculusTransformationGeometric Construction
This example demonstrates the generation of solids of revolution by rotating a rectangle around an axis. Key math concepts include solids of revolution, geometric mean, arithmetic operations, variance, and similarity transformations. It is constructed using GeoGebra commands like Point, Ellipse, Intersect, Vector, Translate, Polygon, Mirror, and Segment. Suitable for high school and above students learning about volume calculations of rotated solids and geometric transformations in calculus.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A_1
  2. Point(yAxis) → D_1
  3. Ellipse(B_1, C_1, D_1) → c
  4. Intersect(xAxis, yAxis) → E
  5. Point(yAxis) → F
  6. Ellipse(G, H, E) → d
  7. Point(c) → A
  8. Vector(A_1, F) → u
  9. Translate(A, u) → B
  10. Polygon(A_1, A, B, F) → poly1, a, i, i', f
  11. Mirror(A, A_1) → D
  12. Mirror(B, F) → C
  13. Polygon(A, B, C, D) → poly2, i_1, i'_1, i'', i'_2
  14. Point(c) → I
  15. Point(c) → J
  16. Point(d) → K
  17. Point(d) → L
  18. Segment(J, L) → b
  19. Segment(I, K) → e