积极 AI Logo 积极 AI

圆锥表面积计算与展开

圆锥表面积计算与展开
几何画板及绘图内容加载中，请稍等……
2020-03-29 06:31
圆立体几何几何作图
①本范例演示圆锥的表面积计算公式及展开图；②涉及核心数学概念包括圆锥的底面积、侧面积、表面积公式、几何展开图；③作图要点：使用 GeoGebra 命令如 If, Conic, Segment, Midpoint, Point, Distance, Rotate, CircleSector, Polygon, Intersect, Arc, Circumference, Angle, CircumcircleArc, Textfield 等构建圆锥模型、计算参数并生成展开图；④适合高中阶段学生复习圆锥几何性质及表面积计算，也可用于几何直观教学。

GeoGebra 命令及参数

  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