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Demonstrating Cone Volume Calculation

Demonstrating Cone Volume Calculation
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2018-01-12 04:48
TrigonometrySolid GeometryGeometric ConstructionSlider Animation
This example demonstrates how to calculate the volume of a cone dynamically. Core mathematical concepts include the cone volume formula, pi, geometric transformations, and parametric equations. The construction utilizes GeoGebra commands and objects like If, Conic, Segment, Midpoint, Point, Distance, Rotate, CircleSector, Polygon, Intersect, Arc, Circumference, Angle, CircumcircleArc, and Textfield to visually show how the volume changes with the base radius and height. Suitable for high school solid geometry teaching, helping students intuitively understand the volume calculation formula and its derivation process.

GeoGebra Commands & Parameters

  1. If(net < -1, (((-net) - 1) * 3), 0) → net_θ
  2. If(net < -1, (3 * ((-net) - 1)) + 0.2, 0.2) → net_b
  3. If(net < -1, -1, net) → net_e
  4. If(net_e > -0.001, 0, (-net_e)) → net_h
  5. Conic(A, B, C, D, E) → c
  6. If(net > 0, 1, 0) → net_1
  7. Conic(A, B, C, D, E) → d
  8. Segment(V, A') → b
  9. Segment(V, F') → e
  10. Midpoint(A', F') → M_{A'F'}
  11. Point(c) → G
  12. Conic(A', B', C', F', E') → k
  13. Conic(A', B', C', F', E') → p
  14. Distance(O, V) → distanceOV
  15. Segment(O_c, O_u) → l
  16. Rotate(O_o, (θ * 2), V) → H
  17. Rotate(O_o, ((-θ) * 2), V) → H'
  18. CircleSector(V, H', H) → q
  19. Polygon(V, A', F') → poly1, f', v, a
  20. Distance(V, H') → distanceVH'
  21. Segment(V, H) → b'
  22. Segment(V, H') → e'
  23. Intersect(p, b') → K, K_2
  24. Intersect(p, e') → J, J_2
  25. Segment(V, J_2) → g
  26. Segment(V, K_2) → i
  27. Arc(p, A', K_2) → t
  28. Arc(p, J_2, F') → f
  29. If(θ + (0.6 * θ_d) < (((2 * π) * r / l_s) * 0.5), θ + (0.6 * θ_d), (((2 * π) * r / l_s) * 0.5)) → θ_c
  30. Rotate(O_o, θ_c, V) → H_1
  31. Rotate(O_o, (-θ_c), V) → H'_1
  32. CircleSector(V, H'_1, H_1) → c_2
  33. Circumference(c_2) → j
  34. Circumference(c) → circumferencec
  35. Distance(V, H'_1) → distanceVH'1
  36. Angle(H'_1, V, H_1) → α
  37. Point(c_2) → I
  38. CircumcircleArc(H', O_o, H) → c_1
  39. CircleSector(V, H'_1, H_1) → s
  40. Segment(M_{A'F'}, F') → m
  41. Segment(M_{A'F'}, V) → n
  42. Angle(F', M_{A'F'}, V) → β
  43. Midpoint(b) → M_{VA'}
  44. Textfield(r) → inputBox1
  45. Textfield(h) → inputBox2