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Net of a Cone by Michael Bailey

Net of a Cone by Michael Bailey
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2015-04-07 09:57
Coordinate GeometrySolid GeometryGeometric Construction
In collections Chapter 11: Surface Area and Volume
This example demonstrates the net of a cone. It involves cone geometry, coordinate geometry, and geometric construction. Using GeoGebra commands such as OrthogonalLine, Circle, Intersect, etc., the net of a cone can be constructed. Suitable for middle and high school students to learn cone geometry and solid geometry.

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
  22. Segment((2, 0, 0), G) → i
  23. Midpoint(p) → H
  24. Point(xAxis) → I
  25. Cone(I, J, 1) → o, q, s

AI Drawing Prompt Reference

Draw the net of a cone. Start with a base circle in a horizontal planehol and a point above its center as the apex. Connect the apex to the center to form the slant height. Rotate the apex around the vertical axis by a certain angle to define the unfolded cone surface. On the unfolded plane, draw a circular arc centered at the rotated apex with radius equal to the slant height, representing the outer edge of the sector. Add the two straight edges of the sector and the arc corresponding to the base circle. Finally, include a full 3D cone beside the net, with labels for base radius, slant height, and the sector angle.
The prompt above was compiled from the original drawing commands and is for reference only.