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Forming a Cone with Cylinder Dimensions

Forming a Cone with Cylinder Dimensions
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2017-05-04 01:07
CircleSolid GeometryGeometric Construction
This example demonstrates how to form a cone using the height and width of a cylinder on a 2D plane with paper, compass, and ruler. Key math concepts include circumference, vectors, and rotation. Construction highlights involve GeoGebra commands like Cone, Circumference, Circle, Distance, Vector, Segment, Polygon, Cylinder, Angle, PointIn, Plane, Rotate, CircleSector, and CircleArc. Suitable for high school and above, focusing on solid geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Cone(C_0, C_h, r_i) → Cone_i, c_iCone, ConeSurface
  2. Circumference(c_iCone) → pi_dCone
  3. Circle(circle_1, O, W_i) → circle_2Slice
  4. Circumference(circle_2Slice) → pi_dCircleEnd
  5. Distance(C_h, circle_1) → slant
  6. Vector(O, C_0) → r
  7. Vector(W_i, O) → diameter
  8. Vector(O, H_i) → h_YaxisUp
  9. Vector(H_i, O) → h_yAxisDown
  10. Segment(O, H_i) → h_yAxis
  11. Vector(H_i, EdgeOfCylinder) → u_1
  12. Vector(EdgeOfCylinder, H_i) → diameter_rev
  13. Segment(H_i, EdgeOfCylinder) → d
  14. Vector(W_i, EdgeOfCylinder) → h_edge
  15. Vector(EdgeOfCylinder, W_i) → v_1
  16. Polygon(O, H_i, EdgeOfCylinder, W_i) → Two_dCylinderRep, TwoDCylinderRep_3, TwoDCylinderRep_2, TwoDCylinderRep_1, TwoDCylinderRep_4
  17. Cylinder((1 / 2 * w), (1 / 2 * w) + h, r_i) → Cylinder_1, c_i, c_h, CylinderSurface
  18. Vector(W_i, C_h) → s_1
  19. Vector(O, C_h) → s_2
  20. Polygon(C_h, O, W_i) → Two_dConeFrameAsTriangle, Hypotenuse2_dMiniTriangleL, TwoDCylinderRep_0, o
  21. Angle(C_0, W_i, C_h) → b
  22. Angle(C_h, O, C_0) → b'
  23. Angle(O, C_h, w) → a
  24. Vector(C_0, C_h) → Height_cylinder
  25. Segment(C_0, C_h) → TwoDCylinderRep_h
  26. Angle(C_h, C_0, W_i) → c
  27. Angle(C_h, C_0, O, xOyPlane) → c'
  28. Segment(C_h, w) → s
  29. Segment(O, C_0) → radiusCone
  30. Circumference(circle_2Slice) → pi_dCircleEndSlice
  31. Circle(C_h, slant, xOyPlane) → t
  32. Circumference(t) → pi_dCircleT
  33. PointIn(t) → Pointt
  34. Segment(CutStart, C_h) → CompassLength
  35. Segment(C_h, CutStart) → cutFromLine
  36. Plane(circle_2Slice) → plane_Circle
  37. Rotate(CutStart, (-cutAngleMin), C_h) → CutFrom'
  38. Vector(C_h, CutStart) → v
  39. Vector(C_h, CutFrom') → v'
  40. CircleSector(C_h, CutStart, CutFrom', xOyPlane) → slice
  41. CircleArc(C_h, CutFrom', CutStart, xOyPlane) → ArcLengthDifferenceOfCircumferences
  42. Angle(CutFrom', C_h, CutStart) → θ
  43. CircleSector(C_h, CutFrom', CutStart, xOyPlane) → circle_2SliceInside
  44. Rotate(CutStart, (-ratio360deg), C_h) → CutDont
  45. CircleSector(C_h, CutDont, CutStart, xOyPlane) → e
  46. Angle(CutDont, C_h, CutStart, xOyPlane) → α