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棱柱与圆柱体积计算

棱柱与圆柱体积计算
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2018-04-23 07:19
函数立体几何几何作图
①本范例演示棱柱与圆柱的体积计算方法；②涉及核心数学概念包括体积公式、几何体特性、空间想象能力；③作图要点：使用Point, Ray, Circle, Intersect, Segment, Midpoint, Polygon, OrthogonalLine, OrthogonalPlane, Prism, Cylinder等GeoGebra命令与对象构建几何体并计算体积；④适合高中阶段学生及需要复习立体几何体积知识的用户。

GeoGebra 命令及参数

  1. Point(yAxis) → J_2
  2. Ray(J_2, K_2) → q_2
  3. Circle(J_2, Hbase) → p_2
  4. Intersect(p_2, q_2, 1) → L_2
  5. Segment(J_2, L_2) → j_3
  6. Midpoint(J_2, L_2) → R_2
  7. Polygon(J_2, L_2, 6) → poly2, r_2, P_2, s_2, t_2, a_2, b_2, f_3, M_2, N_2, O_2
  8. Segment(N_2, J_2) → h_3
  9. Segment(O_2, L_2) → g_3
  10. Intersect(g_3, h_3) → Q_2
  11. Segment(Q_2, R_2) → s_4
  12. Intersect(xAxis, yAxis) → A
  13. Circle(A, base) → c
  14. Intersect(c, xAxis, 2) → B
  15. OrthogonalLine(B, xAxis) → f
  16. Circle(A, width) → d
  17. Intersect(d, yAxis, 2) → C
  18. OrthogonalLine(C, yAxis) → g
  19. Intersect(f, g) → D
  20. Polygon(A, B, D, C) → q1, a, b, d_1, c_1
  21. OrthogonalPlane(A, a) → e
  22. Circle(A, height, e) → h
  23. Intersect(zAxis, h) → E, F
  24. Prism(q1, E) → i, G, edgeBG, edgeDH, edgeCI, edgeEG, edgeGH, edgeHI, edgeEI, H, I, faceABGE, faceBDHG, faceCDHI, faceACIE, faceEGHI, edgeAE
  25. Midpoint(I, C) → J
  26. Midpoint(C, D) → K
  27. Midpoint(C, A) → L
  28. Point(xAxis) → M
  29. Circle(M, radius) → k
  30. OrthogonalPlane(M, yAxis) → j
  31. Circle(M, cylinderheight, j) → p
  32. OrthogonalLine(M, xOyPlane) → l
  33. Intersect(l, p) → N, O
  34. Intersect(k, xAxis, 2) → P
  35. Cylinder(M, N, radius) → m, q, r, n
  36. Center(r) → Q
  37. Point(r) → R
  38. OrthogonalLine(R, r) → s
  39. Intersect(s, q) → S,
  40. Midpoint(R, S) → T
  41. Midpoint(M, P) → U
  42. Segment(M, P) → t
  43. Point(xAxis) → V
  44. Circle(V, Tradius) → e_1
  45. Intersect(e_1, xAxis, 1) → W
  46. Intersect(e_1, xAxis, 2) → Z
  47. Polygon(W, A_1, Z) → t1, z_1, w, a_1
  48. OrthogonalLine(A_1, a_1) → f_1
  49. Intersect(f_1, a_1) → E_1
  50. Segment(A_1, E_1) → g_1
  51. Angle(Z, E_1, A_1) → α
  52. OrthogonalLine(W, xOyPlane) → h_1
  53. OrthogonalPlane(W, yAxis) → o
  54. Circle(W, Theight, o) → k_1
  55. Intersect(h_1, k_1) → F_1, G_1
  56. Prism(t1, F_1) → u, H_1, edge4, edge6, edge5, I_1, face3, face4, face2, face1, edge1, edge3, edge2
  57. Segment(W, Z) → i_1
  58. Midpoint(W, Z) → J_1
  59. Point(xAxis) → B_1
  60. Circle(B_1, Tradius2) → p_1
  61. Intersect(p_1, xAxis, 2) → C_1
  62. Intersect(p_1, xAxis, 1) → D_1
  63. Polygon(K_1, C_1, D_1) → t2, d_2, k_2, c_2
  64. OrthogonalLine(K_1, xAxis) → j_1
  65. Intersect(j_1, xAxis) → L_1
  66. Segment(K_1, L_1) → l_1
  67. Angle(K_1, L_1, D_1) → β
  68. Segment(D_1, C_1) → m_1
  69. Midpoint(D_1, C_1) → M_1
  70. OrthogonalLine(K_1, xOyPlane) → n_1
  71. OrthogonalPlane(K_1, xAxis) → v
  72. Circle(K_1, Theight2, v) → q_1
  73. Intersect(n_1, q_1) → N_1, O_1
  74. Prism(t2, N_1) → b_1, P_1, edge10, edge12, edge11, Q_1, face7, face6, face8, face5, edge9, edge7, edge8
  75. Angle(B, A, C) → γ
  76. Angle(A, C, D) → δ
  77. Angle(C, D, B) → ε
  78. Angle(D, B, A) → ζ
  79. Circle(R_1, o_1) → r_1
  80. Point(r_1) → S_1
  81. Segment(R_1, S_1) → s_1
  82. Midpoint(R_1, S_1) → T_1
  83. Polygon(R_1, S_1, 5) → poly1, t_1, f_2, g_2, h_2, i_2, U_1, V_1, W_1
  84. Midpoint(U_1, S_1) → Z_1
  85. Midpoint(W_1, R_1) → A_2
  86. Segment(U_1, A_2) → j_2
  87. Segment(W_1, Z_1) → l_2
  88. Intersect(j_2, l_2) → B_2
  89. Midpoint(R_1, S_1) → C_2
  90. Segment(B_2, C_2) → m_2
  91. Angle(B_2, C_2, R_1) → η
  92. OrthogonalLine(R_1, xOyPlane) → n_2
  93. OrthogonalPlane(R_1, yAxis) → u_1
  94. Circle(R_1, Ptnheight, u_1) → e_2
  95. Intersect(n_2, e_2) → D_2, E_2
  96. Prism(poly1, D_2) → v_1, F_2, face14, edge13, edge14, edge15, edge16, edge17, edge18, edge20, edge21, edge22, G_2, edge19, H_2, I_2, face9, face11, face12, face13, face10
  97. Angle(Q_2, R_2, J_2) → θ
  98. OrthogonalLine(J_2, xOyPlane) → k_3
  99. OrthogonalPlane(J_2, yAxis) → w_1
  100. Circle(J_2, Hheight, w_1) → c_3
  101. Intersect(k_3, c_3) → S_2, T_2
  102. Prism(poly2, S_2) → o_2, U_2, face20, face16, face21, edge23, edge24, edge25, edge26, edge27, edge28, edge29, V_2, edge31, edge32, edge33, edge34, edge30, W_2, Z_2, A_3, face15, face17, face18, face19
  103. Point(yAxis) → B_3
  104. Ray(B_3, C_3) → l_3
  105. Circle(B_3, ORadius) → d_3
  106. Intersect(d_3, l_3, 1) → D_3
  107. Segment(B_3, D_3) → m_3
  108. Polygon(B_3, D_3, 8) → poly3, n_3, F_3, G_3, H_3, I_3, J_3, p_3, q_3, r_3, s_3, t_3, a_3, b_3, E_3
  109. Segment(G_3, B_3) → e_3
  110. Segment(H_3, D_3) → f_4
  111. Intersect(e_3, f_4) → K_3
  112. Midpoint(B_3, D_3) → L_3
  113. Segment(K_3, L_3) → g_4
  114. Angle(K_3, L_3, B_3) → ι
  115. OrthogonalLine(B_3, xOyPlane) → h_4
  116. OrthogonalPlane(B_3, yAxis) → u_2
  117. Circle(B_3, Oheight, u_2) → c_4
  118. Intersect(h_4, c_4) → M_3, N_3
  119. Prism(poly3, M_3) → v_2, O_3, face25, face26, face27, face28, face29, face23, face30, edge35, edge36, edge37, P_3, edge38, edge39, edge40, edge41, edge42, edge43, edge45, edge46, edge47, edge48, Q_3, edge49, edge50, edge44, R_3, S_3, T_3, U_3, face22, face24
  120. Midpoint(Q_2, R_2) → V_3
  121. Midpoint(A_1, E_1) → W_3
  122. Midpoint(K_1, L_1) → Z_3
  123. Midpoint(K_3, L_3) → A_4
  124. Midpoint(B_2, C_2) → B_4
  125. Midpoint(Q_2, R_2) → C_4