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Sphere and Cone Cross Sections

Sphere and Cone Cross Sections
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2018-04-20 21:01
Coordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the cross-sections of a sphere and a cone, showing how their shapes change with different cutting planes. It involves core mathematical concepts like solid geometry, cross-section analysis, and geometric construction. Key GeoGebra commands used include Sphere, Point, Cone, OrthogonalPlane, IntersectPath, Plane, Intersect, and Segment. Suitable for high school geometry teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Sphere((-2, 0, 2), 2) → a
  2. Point(Segment[(0, 0, 4), (0, 0, 0)]) → A
  3. Cone((2, 0, 0), (2, 0, 4), 2) → b, c, d
  4. OrthogonalPlane(A, zAxis) → e
  5. IntersectPath(e, a) → f
  6. IntersectPath(e, b) → g
  7. Plane(zAxis, xAxis) → h
  8. Intersect(h, f) → B, C
  9. Intersect(h, g) → D, E
  10. Segment(C, B) → i
  11. Segment(E, D) → j