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Related Rates: Filling/Draining Cone

Related Rates: Filling/Draining Cone
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2015-11-20 21:28
Solid GeometryCalculusDerivativeGeometric Construction
This example demonstrates the related rates problem involving the filling or draining of a cone, showing how the height of the water changes with respect to the volume. Key math concepts include calculus-related rates, the volume formula for a cone, and derivative applications. The construction utilizes GeoGebra commands like Intersect, Segment, Distance, Mirror, Ellipse, Point, Polygon, OrthogonalLine, Ray, Angle, and Textfield. It is suitable for high school students and above studying calculus and solid geometry, or for educational purposes.

GeoGebra Commands & Parameters

  1. Intersect(a, b) → A
  2. Intersect(c, a) → B
  3. Intersect(c, b) → C
  4. Segment(A, C) → d
  5. Segment(A, B) → e
  6. Segment(C, B) → f
  7. Intersect(f, x = 0) → D
  8. Distance(D, B) → g
  9. Mirror(G, x = 0) → G'
  10. Ellipse(G, G', E) → k
  11. Segment(A, D) → i
  12. Point(i) → H
  13. Intersect(j, d) → I
  14. Intersect(j, e) → J
  15. Distance(H, J) → distanceHJ
  16. Distance(H, J) → l
  17. Mirror(M, x = 0) → M'
  18. Ellipse(M', M, K) → p
  19. Polygon(A, J, I) → poly1, i_1, a_1, j_1
  20. Point(n) → N
  21. OrthogonalLine(N, n) → q
  22. Intersect(c, q) → O
  23. Segment(O, N) → height
  24. Point(c) → P
  25. Ray(C, O) → s
  26. Angle(N, O, C) → α
  27. Ray(B, P) → t
  28. Segment(D, B) → b_1
  29. Textfield(height_1) → InputBox1
  30. Textfield(m) → InputBox2
  31. Textfield(dhdt) → InputBox3
  32. Distance(D, B) → h
  33. OrthogonalLine(H, height) → c_1
  34. Point(n) → Q
  35. OrthogonalLine(Q, c_1) → d_1
  36. Intersect(c_1, d_1) → R
  37. Segment(Q, R) → e_1
  38. Distance(H, J) → o
  39. Segment(A, H) → f_1
  40. Distance(A, H) → u