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Net of a Cone by Cuemath (2)

Net of a Cone by Cuemath (2)
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2019-01-10 18:54
CircleAngleSolid GeometryGeometric ConstructionSlider Animation
This example demonstrates the construction and calculation of the net (sector) of a cone, involving core math concepts like solid geometry, circle, angle, rotation, and geometric construction. It utilizes various GeoGebra commands/objects such as OrthogonalLine, Circle, Point, Intersect, Cone, Segment, Distance, Angle, Rotate, CircumcircleArc, Surface, and CurveCartesian as outlined in the construction summary. Suitable for high school students learning solid geometry and geometric constructions.

GeoGebra Commands & Parameters

  1. OrthogonalLine((1, 0, 0), xOyPlane) → a
  2. Circle(a, (0, 0, 0)) → c
  3. Point(a) → A
  4. Intersect(xAxis, a) → B
  5. Cone(B, A, 1) → b, d, e
  6. Intersect(yAxis, xAxis) → C
  7. Segment(C, A) → l
  8. Distance(B, C) → r
  9. Angle(A, C, B) → α
  10. Rotate(A, (t * α), yAxis) → A'
  11. OrthogonalLine(A', xOyPlane) → f
  12. Intersect(f, xOyPlane) → B'
  13. Rotate(C, β / 2, f) → C'
  14. Rotate(C, ((-β)) / 2, f) → C'_1
  15. CircumcircleArc(C', C, C'_1) → g
  16. Distance(A', B') → h
  17. Distance(B', C') → r'
  18. Surface(((k - ((v * r') * cos((u * β / 2)))) * cos(ϕ)) - (((1 - v) * h) * sin(ϕ)), ((v * r') * sin((u * β / 2))), (((1 - v) * h) * cos(ϕ)) + ((k - ((v * r') * cos((u * β / 2)))) * sin(ϕ)), u, -1, 1, v, 0, 1) → j
  19. CurveCartesian(((k - (r' * cos((u * β / 2)))) * cos(ϕ)), (r' * sin((u * β / 2))), ((k - (r' * cos((u * β / 2)))) * sin(ϕ)), u, -1, 1) → m
  20. Segment(E, F) → n
  21. Segment(D, F) → p