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棱柱与锥体体积对比演示

棱柱与锥体体积对比演示
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2016-06-23 23:28
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本范例演示了底面积和高度相同的棱柱与锥体的体积对比现象；②涉及的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——从下方『构造摘要』提炼用到了Circle（圆）、Segment（线段）、Intersect（交点）、Polygon（多边形）、Plane（平面）、Mirror（镜像）、Prism（棱柱）、Pyramid（锥体）等GeoGebra命令/对象；④适合高中阶段学习立体几何的学生，用于直观理解体积计算公式的应用与对比。

GeoGebra 命令及参数

  1. Circle(center, B, xOyPlane) → c
  2. Segment(center, B) → f
  3. Circle(B, f) → d
  4. Intersect(d, c) → C, D, ,
  5. Circle(D, f, xOyPlane) → e
  6. Circle(C, f, xOyPlane) → g
  7. Intersect(e, c) → E, F, ,
  8. Intersect(g, c) → G, H, ,
  9. Circle(G, f, xOyPlane) → h
  10. Intersect(h, c) → I, J, ,
  11. Polygon(B, D, F, I, G, C) → poly1, b, d_1, f_1, i, g_1, c_1
  12. Plane(L, A, K) → a
  13. Mirror(poly1, a) → hexagon
  14. Prism(hexagon, B) → HexPrism, M, face6, face2, CrossSection, edge1, edge2, edge3, edge4, edge5, edge6, edgeBM, N, edgeMN, edgeNO, edgeOP, edgePQ, edgeBQ, O, P, Q, face1, face3, face4, face5
  15. PointIn(CrossSection) → PointfaceBMNOPQ
  16. Volume(HexPrism) → volumej
  17. Point(HexPrism) → Pointj
  18. PointIn(CrossSection) → PointCrossSection
  19. PointIn(hexagon) → Pointpoly1'
  20. Text(PrismHeight, (x(B) + 0.2, y(B) + 0.5)) → text1
  21. Plane(R, a) → j
  22. Plane(S, a) → k
  23. Plane(T, a) → l
  24. Plane(U, a) → m
  25. Plane(V, a) → n
  26. Midpoint(edgeBQ) → W
  27. Segment(center, W) → p
  28. Angle(B, W, center, xOyPlane) → α
  29. Textfield(calc) → Calculator
  30. Pyramid(hexagon, center) → Pyramid, face7, edge10, edge11, edge12, face9, face10, face11, face12, face8, edge7, edge8, edge9
  31. Volume(Pyramid) → volumePyra
  32. Point(Pyramid) → PointPyra
  33. Segment(B, W) → q