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Curved Surface Area of Cones Demo

Curved Surface Area of Cones Demo
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2020-05-09 01:30
TrigonometrySolid GeometryGeometric Construction
In collections Geometry - Areas and Volumes
This example demonstrates how the curved surface area of a cone equals a sector. It involves core math concepts like surface area, sector geometry, Pythagorean theorem, and algebra. Constructed using GeoGebra commands such as Point, Circle, Intersect, Rotate, Mirror, Segment, CircumcircleArc, Surface, and Vector. Ideal for high school students and math enthusiasts to visualize and understand the geometric principles behind cone surface area calculations.

GeoGebra Commands & Parameters

  1. Point(zAxis) → A
  2. Point(Segment[A, (0, 0, 0)]) → P
  3. Point(xAxis) → B
  4. Circle(P, Distance[A, B], yAxis) → c
  5. Intersect(xOyPlane, c) → C, D
  6. Intersect(xAxis, yAxis) → O
  7. Rotate(D, γ, zAxis) → D_1
  8. Rotate(D_1, α, zAxis) → D'
  9. Rotate(D_1, (π * x(B) / x(D)), zAxis) → D'_1
  10. Mirror(D'_1, O) → E
  11. Segment(P, D') → e
  12. Circle(zAxis, B) → g
  13. CircumcircleArc(D_1, E, D') → h
  14. CircumcircleArc(D_1, D'_1, D') → d
  15. Segment(P, D_1) → b
  16. Surface((u * cos(v)), (u * sin(v)), f(u), u, 0, x(D), v, γ, (2 * π) - γ) → a
  17. Vector(A + (0, 0, 1), A + (0, 0, 0.2)) → u
  18. Segment(O, A) → i
  19. Segment(O, B) → j

AI Drawing Prompt Reference

Draw the lateral surface of a cone, including the center of the base O, the vertex A, points D and D' on the circumference of the base, and the arc D'_1 and E generated by rotating D'. Create a cylinder using points A and B, then draw the curved surface of the cone, using rotation and mirroring to generate the cone's lateral surface展开图。
The prompt above was compiled from the original drawing commands and is for reference only.