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Adjustable Cone Related Rates Demo

Adjustable Cone Related Rates Demo
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2016-10-25 06:15
TrigonometrySolid GeometryCalculus
This example demonstrates the dynamic relationship between height, height-to-radius ratio, and rate of height change in an adjustable cone, focusing on calculus-related rates problems. Core math concepts include calculus, solid geometry (cone volume/surface area), and trigonometric applications. Constructed using GeoGebra commands like Cone, Polygon, Segment, Angle, Distance, Translate, Textfield, and FractionText to model the cone and related geometric elements. Ideal for high school students and teachers exploring calculus applications, geometric modeling, and parametric animations.

GeoGebra Commands & Parameters

  1. Cone(B, A, h / p) → a, c, b
  2. Cone(C, A, 20) → d, e, f
  3. Polygon(A, D, E) → poly1, e_1, a_1, d_1
  4. Polygon(A, F, G) → poly2, g_1, a_2, f_1
  5. Segment(D, E) → i
  6. Angle(A, F, G, xOyPlane) → α
  7. Angle(A, D, E, xOyPlane) → β
  8. Distance(D, E) → distanceDE
  9. Distance(F, G) → distanceFG
  10. Segment(I, D) → j
  11. Translate(A, Vector[(-3, 0)]) → A'
  12. Translate(F, (-3, 0)) → F'
  13. Segment(A', F') → k
  14. Distance(A', F') → distanceA'F'
  15. Distance(I, i) → distanceIi
  16. Textfield(h) → InputBox1
  17. Textfield(p) → InputBox2
  18. FractionText(p) → text4