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棱柱体积计算 by Will Wassell

棱柱体积计算 by Will Wassell
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2016-03-10 19:45
立体几何几何作图
①本范例演示棱柱体积的计算方法；②涉及核心数学概念包括体积公式、多边形面积、空间几何；③构造要点：使用Intersect, Point, Polygon, Prism, Cylinder等命令创建棱柱模型，通过face, edge, text等对象展示计算过程；④适合高中立体几何教学或自学，帮助理解体积计算原理。

GeoGebra 命令及参数

  1. Intersect(yAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(yAxis) → D
  4. Polygon(A, B, C, D) → poly1, a, b, c, d
  5. Point(zAxis) → H
  6. Prism(poly1, H) → e, E, edgeBE, edgeCF, edgeDG, edgeEH, edgeEF, edgeFG, edgeGH, F, G, faceABEH, faceBCFE, faceCDGF, faceADGH, faceEFGH, edgeAH
  7. Point(xAxis) → I
  8. Prism(I, J, K, N) → f, L, edgeIK, edgeIN, edgeJL, edgeKM, edgeLN, edgeLM, edgeMN, M, faceIJK, faceIJLN, faceJKML, faceIKMN, faceLMN, edgeIJ, edgeJK
  9. Prism(O, P, Q, R, S, T, B_1) → g, U, faceRSZW, face3, face2, face4, edgeOP, edgePQ, edgeQR, edgeRS, edgeST, edgeOT, V, edge1, edgePU, edgeQV, edgeRW, edgeSZ, edge2, edge3, edgeUV, edgeVW, edgeWZ, W, edge5, edge4, Z, A_1, faceOPQRST, face1, facePQVU, faceQRWV
  10. Point(yAxis) → C_1
  11. Point(yAxis) → D_1
  12. Cylinder(C_1, D_1, 4) → h, k, p, i
  13. Point(yAxis) → I_1
  14. Polygon(G_1, H_1, I_1, J_1, E_1, F_1) → poly2, g_1, h_1, i_1, j_1, e_1, f_1
  15. Prism(poly2, l) → m, Q_1, face13, face12, face14, face18, edge20, edge21, edge22, edge23, edge18, edge19, R_1, edge24, edge26, edge27, edge28, edge29, edge25, S_1, T_1, U_1, V_1, face15, face16, face17