Volume of Cone by Kent Tsang

Volume of Cone by Kent Tsang
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2017-05-09 16:58
This example demonstrates how to generate a cone by rotation and calculate its volume. Key mathematical concepts include the volume formula of a cone and rotation geometry. Using GeoGebra commands such as If, Conic, Segment, Midpoint, etc., the net of the cone and volume calculation are constructed. Suitable for high school mathematics education and learning.

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

AI Drawing Prompt Reference

Draw a cone by first creating its net, then rotating it to form the 3D shape. Set the radius of the base and height, and calculate the volume of the cone. Key objects include the base radius, height, net, and side surface of the cone.
The prompt above was compiled from the original drawing commands and is for reference only.