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Cone Total Surface Area Calculator and Net

Cone Total Surface Area Calculator and Net
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2020-03-29 06:31
CircleSolid GeometryGeometric Construction
This example demonstrates the calculation of a cone's total surface area and its net. It involves core mathematical concepts such as base area, lateral surface area, total surface area formulas, and geometric net construction. The construction uses GeoGebra commands like If, Conic, Segment, Midpoint, Point, Distance, Rotate, CircleSector, Polygon, Intersect, Arc, Circumference, Angle, CircumcircleArc, and Textfield to build the cone model, calculate parameters, and generate the net. It is suitable for high school students reviewing cone geometry and surface area calculations, as well as for geometric visualization teaching.

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