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Prism & Cylinder Volume Calculation

Prism & Cylinder Volume Calculation
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2018-04-23 07:19
FunctionSolid GeometryGeometric Construction
This example demonstrates the calculation methods for the volumes of prisms and cylinders. It involves core mathematical concepts such as volume formulas, geometric properties, and spatial visualization skills. Key GeoGebra commands and objects used in construction include Point, Ray, Circle, Intersect, Segment, Midpoint, Polygon, OrthogonalLine, OrthogonalPlane, Prism, Cylinder, etc. Suitable for high school students and users needing to review solid geometry volume concepts.

GeoGebra Commands & Parameters

  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