Related Rates: Adjustable Cone

Related Rates: Adjustable Cone
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2016-10-27 09:54
This example demonstrates an adjustable cone where the height-to-radius ratio can be adjusted while keeping the volume rate of change constant. The core mathematical concept involves related rates in calculus. Using GeoGebra commands such as Dilate, Line, and Intersect, the shape of the cone can be dynamically adjusted. Suitable for high school and above students to learn about related rates.

GeoGebra Commands & Parameters

  1. Dilate(A, If[0 < t ≤ 1, 1 - t, 0], B) → A'
  2. Line(A, C) → f
  3. Intersect(a, f) → R
  4. Cone(A', A, Distance[A', R]) → b, c, d
  5. Dilate(B, If[1 < t ≤ 2, 2 - t, 0], D) → B'
  6. Intersect(e, f) → S
  7. Cone(B', A, Distance[B', S]) → g, h, i
  8. Dilate(D, If[2 < t ≤ 3, 3 - t, 0], F) → D'
  9. Intersect(j, f) → T
  10. Cone(D', A, Distance[D', T]) → l, q, m
  11. Dilate(F, If[3 < t ≤ 4, 4 - t, 0], H) → F'
  12. Intersect(n, f) → U
  13. Cone(F', A, Distance[F', U]) → o, r, s
  14. Dilate(H, If[4 < t ≤ 5, 5 - t, 0], J) → H'
  15. Intersect(u, f) → V
  16. Cone(H', A, Distance[H', V]) → v, c_1, w
  17. Dilate(J, If[5 < t ≤ 6, 6 - t, 0], L) → J'
  18. Intersect(a_1, f) → W
  19. Cone(J', A, Distance[J', W]) → b_1, d_1, e_1
  20. Dilate(L, If[6 < t ≤ 7, 7 - t, 0], N) → L'
  21. Intersect(f, f_1) → Z
  22. Cone(L', A, Distance[L', Z]) → g_1, h_1, i_1
  23. Dilate(N, If[7 < t ≤ 8, 8 - t, 0], P) → N'
  24. Intersect(j_1, f) → A_1
  25. Cone(N', A, Distance[N', A_1]) → k_1, p_1, l_1
  26. Textfield(k) → InputBox1
  27. Textfield(p) → InputBox2
  28. Cone(P, A, Radius[p_1]) → o_1, q_1, r_1
  29. Textfield(t) → InputBox3
  30. Height(o_1) → b_2
  31. Textfield(c_2) → InputBox4
  32. Cone((0, 0, c_2), A, c_2 / p) → d_2, e_2, f_2

AI Drawing Prompt Reference

Draw an adjustable cone with a slider to control the height-to-radius ratio while maintaining a constant volume rate of change. Use dynamic transformation tools to adjust the cone's shape, showing the dynamic process of the cone's transformation, suitable for learning calculus concepts of related rates.
The prompt above was compiled from the original drawing commands and is for reference only.