几何棱柱体积计算演示

几何棱柱体积计算演示
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2019-03-07 11:27
①本范例演示了如何通过 GeoGebra 构建并计算三棱柱的体积;②涉及的核心数学概念包括立体几何、棱柱体积公式、三角形面积计算、二次方程及切线;③作图要点提炼自构造摘要,使用了 Prism、点对象(A-H, I-K)、面对象(faceABCD等)、边对象(edgeAB等)、滑块(L, M)及图形(b, N-O);④适合高中立体几何、解析几何及微积分教学,用于可视化理解体积计算与函数应用。

GeoGebra 命令及参数

  1. Prism(A, B, C, D, E) → a, I, edgeAB, edgeBC, edgeCD, edgeAD, edgeAE, edgeBI, edgeCJ, edgeDK, edgeEI, edgeIJ, J, edgeJK, edgeEK, K, faceABCD, faceABIE, faceBCJI, faceCDKJ, faceADKE, faceEIJK
  2. Prism(F, M, B, E) → b, N, edge3, edge4, edge5, edge6, edge7, edge8, edge9, O, face1, face2, face3, face4, face5, edge1, edge2
  3. Prism(P, D, G, Q) → c, R, edgeGP, edgePQ, edgeDR, edgeGS, edgeQR, edgeRS, edgeQS, S, faceDGP, faceDPQR, faceDGSR, faceGPQS, faceQRS, edgeDP, edgeDG
  4. Prism(T, C, H, U) → d, V, edgeHT, edgeTU, edgeCV, edgeHW, edgeUV, edgeVW, edgeUW, W, faceCHT, faceCTUV, faceCHWV, faceHTUW, faceUVW, edgeCT, edgeCH
  5. Prism(Z, F, B, A_1) → e, B_1, edgeBZ, edge12, edge11, edge10, edge13, edge15, edge14, C_1, faceBFZ, face9, face7, face8, face6, edgeFZ, edgeBF