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Volume of a Cylinder Inscribed in a Cone

Volume of a Cylinder Inscribed in a Cone
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2017-08-05 20:09
Solid GeometryCalculusOptimizationGeometric ConstructionGraphing
This example demonstrates the volume variation of a cylinder inscribed in a cone. Key math concepts include solid geometry, volume calculation, and functional relationships. Construction highlights involve commands/objects like Point, Circle, Cone, Segment, Cylinder, Volume, PointIn, Plane, IntersectPath, Corner, Locus, Extremum in GeoGebra. Suitable for high school mathematics teaching and geometric construction learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(zAxis, A) → c
  3. Point(zAxis) → B
  4. Cone(c, z(B)) → a, d, b
  5. Segment(B, A) → f
  6. Point(f) → C
  7. Circle(zAxis, C) → e
  8. Cylinder(e, (-z(C))) → g, h, i
  9. Volume(g) → volumeg
  10. PointIn(xOyPlane) → PointxOyPlane_1
  11. Volume(a) → volumea
  12. PointIn(xOyPlane) → PointxOyPlane
  13. Plane(xAxis, zAxis) → j
  14. IntersectPath(j, g) → k
  15. Corner(k) → D, E, F, G
  16. IntersectPath(j, a) → p
  17. Corner(p) → H, I, J, K
  18. Locus(L, C) → loc1
  19. Extremum(q) → M, N