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Cone's Cross Section

Cone's Cross Section
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2020-03-04 23:34
Coordinate GeometrySolid GeometryGeometric Construction
In collections Cross Sections
This example demonstrates the cross section of a cone. Key mathematical concepts include solid geometry and coordinate geometry. Using GeoGebra commands such as Intersect, Point, and Cone, the cross section of a cone can be constructed. Suitable for high school students or educators.

GeoGebra Commands & Parameters

  1. Intersect(yAxis, xAxis) → A
  2. Point(zAxis) → F
  3. Intersect(zAxis, xAxis) → E
  4. Cone(E, F, 1) → TheCone, r, i
  5. PointIn(i) → G
  6. Point(xAxis) → I
  7. Point(xAxis) → K
  8. Point(zAxis) → O
  9. Plane(I, K, O) → p
  10. PointIn(p) → CenterOfNormalAngle
  11. Line(CenterOfNormalAngle, xAxis) → g
  12. Circle(CenterOfNormalAngle, 0.25, p) → c
  13. Intersect(g, c) → i_{2}, i_1
  14. CircleArc(CenterOfNormalAngle, i_{2}, i_1, p) → ArcForPlaneAngle
  15. Point(ArcForPlaneAngle) → NormalAngleHandle
  16. Segment(CenterOfNormalAngle, NormalAngleHandle) → NormalSeg
  17. Point(zAxis) → B
  18. Circle(CenterOfNormalAngle, 0.25, p) → d
  19. Point(yAxis) → J
  20. Plane(I, J, K) → q
  21. OrthogonalLine(CenterOfNormalAngle, g, p) → h
  22. Point(zAxis) → C
  23. Cylinder(A, C, 1) → TheCylinder, e, f, b
  24. OrthogonalPlane(G, NormalSeg) → PerPenPlane
  25. IntersectPath(PerPenPlane, TheCone) → k

AI Drawing Prompt Reference

Draw the cross-section of a cone, showing its intersection points with coordinate axes and the relationship between the cross-section. First, plot the coordinate axes and mark key intersection points, then construct the cone and determine its cross-sectional circle. Next, establish the normal angle using the cross-sectional circle and axes, and draw the normal segment and arc. Finally, add a cylinder intersecting the cone and draw the intersection path, fully demonstrating the geometric relationship between the cross-section and the cone.
The prompt above was compiled from the original drawing commands and is for reference only.