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金字塔体积计算

金字塔体积计算
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2019-08-16 19:23
立体几何几何作图
①本范例演示金字塔体积的计算方法；②涉及核心数学概念包括体积公式、多边形面积计算、立体几何；③构造要点：使用Point, Cube, Net, Polygon, Pyramid等命令创建金字塔模型，涉及对象a, A, B, C, cube等；④适合高中数学教学，用于理解体积计算公式及三维图形构建。

GeoGebra 命令及参数

  1. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  2. Cube(A, B, C) → cube, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC, edgeCD, edgeAE, edgeDH, edgeEH, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  3. Net(cube, b) → c, I, R, S, T, U, V, faceIJKL, faceILNM, faceIJRQ, faceJKTS, faceKLVU, J, faceMNOP, edgeIL, edgeIJ, edgeJK, edgeKL, edgeLN, edgeMN, edgeIM, edgeIQ, edgeQR, K, edgeJR, edgeJS, edgeST, edgeKT, edgeKU, edgeUV, edgeLV, edgeNO, edgeOP, edgeMP, L, M, N, O, P, Q
  4. Polygon(B, C, T, S) → pol1, f, g, i, j
  5. Pyramid(pol1, (-h)) → pyr1, W, faceBCW, faceCTW, faceSTW, faceBSW, edgeBW, edgeCW, edgeTW, edgeSW
  6. Polygon(C, D, V, U) → pol2, c_1, d, v, u
  7. Pyramid(pol2, (-h)) → pyr2, Z, face1, face2, face3, face4, edge1, edge2, edge3, edge4
  8. Polygon(D, I, M, N) → pol3, d_1, i_1, m, n
  9. Pyramid(pol3, (-h)) → pyr3, A_1, face5, face6, face7, face8, edge5, edge6, edge7, edge8
  10. Polygon(M, N, O, P) → pol4, m_1, n_1, o, p
  11. Pyramid(pol4, h) → pyr4, B_1, face9, face11, face12, face10, edge9, edge10, edge11, edge12
  12. Polygon(B, R, Q, I) → pol5, b_1, r, q, i_2
  13. Pyramid(pol5, (-h)) → pyr5, C_1, face14, face16, face15, face13, edge13, edge16, edge15, edge14
  14. Polygon(B, C, D, I) → pol6, b_2, c_2, d_2, i_3
  15. Pyramid(pol6, h) → pyr6, D_1, face17, face19, face20, face18, edge17, edge18, edge19, edge20

AI 绘图提示语参考

绘制一个金字塔体积计算模型。首先建立一个立方体，然后展开其表面，接着在展开的面上分别绘制四个三角形，每个三角形作为底面，向上构建四个金字塔。最后，确保所有金字塔的顶点在立方体的中心下方或上方，形成一个完整的金字塔体积模型。
以上提示语为根据原始绘图命令整理而来，仅供参考。