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棱柱体积与底面积关系演示

棱柱体积与底面积关系演示
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2016-06-22 23:50
立体几何几何作图
所属专题 Geo&Alg:Area Volume Pythagorean Th. CCSS G-GMD Geometric Measurement and Dimension
①本范例演示固定底面积时不同棱柱体积的变化规律；②涉及核心概念：棱柱体积公式、底面积恒定、立体几何；③作图要点：使用Point、Segment、Polygon、Prism、Volume等命令构建棱柱模型，通过Slider动态调整参数；④适合高中立体几何教学，用于理解体积与底面积的关系。

GeoGebra 命令及参数

  1. Point(Circle[A, sqrt((4 * AreaBase / tan(60°)))]) → B
  2. Segment(A, B) → f
  3. Polygon(A, B, 3) → reg3, g, h, i, C
  4. Point(Circle[A, AreaBase / sqrt(AreaBase)]) → D
  5. Segment(A, D) → j
  6. Polygon(A, D, 4) → reg4, k, l, m, n, E, F
  7. Point(Circle[A, sqrt((4 * AreaBase / sqrt(25 + (10 * sqrt(5)))))]) → G
  8. Segment(A, G) → p
  9. Polygon(A, G, 5) → reg5, q, r, s, t, a, H, I, J
  10. Point(Circle[A, sqrt(((2 * AreaBase)) / ((3 * sqrt(3))))]) → K
  11. Segment(A, K) → b
  12. Polygon(A, K, 6) → reg6, c, O, d, e, f_1, g_1, h_1, L, M, N
  13. Point(Circle[A, sqrt(AreaBase / (2 + (2 * sqrt(2))))]) → P
  14. Segment(A, P) → i_1
  15. Polygon(A, P, 8) → reg8, j_1, R, S, T, U, V, k_1, l_1, m_1, n_1, p_1, q_1, r_1, Q
  16. Prism(reg3, top) → TriPrism, W, edgetopW, edgeWZ, edgetopZ, Z, faceABWtop, faceBCZW, faceACZtop, facetopWZ, edgeAtop_1, edgeBW, edgeCZ
  17. Prism(reg4, top) → SqPrism, A_1, edge1, edge2, edge3, edge4, edge6, edge7, edge5, B_1, C_1, face1, face3, face4, face2, face5, edgeAtop_2
  18. Prism(reg5, top) → PentPrism, D_1, face11, edgeAtop_3, edge8, edge9, edge10, edge11, edge12, edge14, edge15, edge16, E_1, edge13, F_1, G_1, face6, face8, face9, face10, face7
  19. Prism(reg6, top) → HexPrism, H_1, face17, face13, face18, edgeAtop_4, edge17, edge18, edge19, edge20, edge21, edge22, I_1, edge24, edge25, edge26, edge27, edge23, J_1, K_1, L_1, face12, face14, face15, face16
  20. Prism(reg8, top) → OctPrism, M_1, face22, face23, face24, face25, face26, face20, face27, edgeAtop, edge28, edge29, N_1, edge30, edge31, edge32, edge33, edge34, edge35, edge37, edge38, edge39, edge40, O_1, edge41, edge42, edge36, P_1, Q_1, R_1, S_1, face19, face21
  21. Volume(OctPrism) → volumeOctPrism
  22. Point(OctPrism) → PointOctPrism_1
  23. Volume(HexPrism) → volumeHexPrism
  24. Point(HexPrism) → PointHexPrism_1
  25. Volume(TriPrism) → volumeTriPrism
  26. Point(TriPrism) → PointTriPrism
  27. Volume(SqPrism) → volumeSqPrism
  28. Point(SqPrism) → PointSqPrism
  29. Volume(HexPrism) → o
  30. Point(HexPrism) → PointHexPrism
  31. Volume(OctPrism) → u
  32. Point(OctPrism) → PointOctPrism
  33. Volume(PentPrism) → volumePentPrism
  34. Point(PentPrism) → PointPentPrism_1
  35. Volume(PentPrism) → v
  36. Point(PentPrism) → PointPentPrism