正方锥体积计算

正方锥体积计算
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2017-05-05 08:50
①本范例演示正方锥体积的计算方法与公式应用;②涉及核心数学概念包括立体几何体积公式、正方体与锥体的关系、相似变换;③作图要点:使用Point, Segment, Polygon, Prism, Net, Pyramid等命令构造正方锥及其展开图,通过对象a, A, B, f, poly1, g, h, i, j, C, D, b, E, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH等展示几何关系;④适合高中立体几何教学与体积计算练习。

GeoGebra 命令及参数

  1. Point(Circle[A, a]) → B
  2. Segment(A, B) → f
  3. Polygon(A, B, 4) → poly1, g, h, i, j, C, D
  4. Prism(poly1, a) → b, E, edgeAE, edgeBF, edgeCG, edgeDH, edgeEF, edgeFG, edgeGH, edgeEH, F, G, H, faceABFE, faceBCGF, faceCDHG, faceADHE, faceEFGH
  5. Net(b, c) → d, I, R, S, T, U, V, faceIJKL, faceIJNM, faceJKPO, faceKLRQ, faceILST, J, faceMNUV, edgeIJ, edgeJK, edgeKL, edgeIL, edgeIM, edgeMN, edgeJN, edgeJO, edgeOP, K, edgeKP, edgeKQ, edgeQR, edgeLR, edgeLS, edgeST, edgeIT, edgeNU, edgeUV, edgeMV, L, M, N, O, P, Q
  6. Pyramid(faceMNUV, (-(a / 2))) → e, W, faceMNW, faceNUW, faceUVW, faceMVW, edgeMW, edgeNW, edgeUW, edgeVW
  7. Pyramid(faceIJNM, (-(a / 2))) → k, Z, faceIJZ, faceJNZ, faceMNZ, faceIMZ, edgeIZ, edgeJZ, edgeNZ, edgeMZ
  8. Pyramid(faceIJKL, a / 2) → l, A_1, face1, face3, face4, face2, edge1, edge2, edge3, edge4
  9. Pyramid(faceJKPO, (-(a / 2))) → m, B_1, face5, face7, face8, face6, edge5, edge6, edge8, edge7
  10. Pyramid(faceILST, (-(a / 2))) → n, C_1, face9, face10, face12, face11, edge10, edge9, edge12, edge11
  11. Pyramid(faceKLRQ, (-(a / 2))) → o, D_1, face13, face15, face16, face14, edge13, edge14, edge16, edge15
  12. Point(Circle[E_1, a]) → F_1
  13. Segment(E_1, F_1) → p
  14. Polygon(E_1, F_1, 4) → poly2, q, r, s, t, G_1, H_1
  15. Prism(poly2, a) → u, I_1, edge17, edge18, edge19, edge20, edge21, edge23, edge24, edge22, J_1, K_1, L_1, face17, face19, face20, face18, face21

AI 绘图提示语参考

绘制一个正方形金字塔,包括底面正方形、侧面四个三角形和金字塔的展开图。首先画出底面正方形,然后构造四个侧面三角形,最后画出金字塔的展开图,展示几何关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。