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立方体与长方体的表面积和体积

立方体与长方体的表面积和体积
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2015-02-02 08:13
立体几何几何作图
所属专题 Area-Volumen-Algebra-inequalities-Trigonometric
①本范例演示立方体与长方体的表面积和体积计算；②涉及核心数学概念：面积公式（面面积=边长²）、体积公式（体积=边长³）；③作图要点：使用 GeoGebra 命令如 Intersect（相交）、Point（点）、Cube（立方体）等构建几何体及关键点、面、边；④适合初中及以上学生学习立体几何及空间想象能力。

GeoGebra 命令及参数

  1. Intersect(yAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[B, Distance[A, B], Segment[A, B]]) → C
  4. Cube(A, B, C) → a, D, faceCDHG, faceEFGH, edgeAD, edgeAB, edgeBC_1, edgeCD, edgeAE, edgeDH, edgeEH_1, edgeEF, E, edgeBF, edgeFG, edgeCG, edgeGH, F, G, H, faceABCD, faceADHE, faceABFE, faceBCGF
  5. Point(Circle[B, Distance[C, B], Segment[C, B]]) → I
  6. Cube(C, B, I) → b, J, faceIJNM, faceKLMN, edgeCJ, edgeBC, edgeBI, edgeIJ_1, edgeCK, edgeJN, edgeKN, edgeKL, K, edgeBL, edgeLM, edgeIM, edgeMN, L, M, N, faceBCJI, faceCJNK, faceBCKL, faceBIML
  7. Point(Circle[I, Distance[J, I], Segment[J, I]]) → O
  8. Cube(J, I, O) → c, P, faceOPTS, faceQRST, edgeJP, edgeIJ, edgeIO, edgeOP_1, edgeJQ, edgePT, edgeQT, edgeQR, Q, edgeIR, edgeRS, edgeOS, edgeST, R, S, T, faceIJPO, faceJPTQ, faceIJQR, faceIOSR
  9. Point(Circle[O, Distance[P, O], Segment[P, O]]) → U
  10. Cube(P, O, U) → d, V, face3, face4, edgePV, edgeOP, edgeOU, edgeUV_1, edgePW, edge2, edge3, edgeWZ, W, edgeOZ, edge4, edge1, edge5, Z, A_1, B_1, faceOPVU, face2, faceOPWZ, face1
  11. Point(Circle[U, Distance[V, U], Segment[V, U]]) → C_1
  12. Cube(V, U, C_1) → e, D_1, face9, face10, edge8, edgeUV, edge6, edge10, edge9, edge12, edge14, edge13, E_1, edge7, edge15, edge11, edge16, F_1, G_1, H_1, face5, face8, face6, face7
  13. Point(Circle[E, Distance[H, E], Segment[H, E]]) → I_1
  14. Cube(H, E, I_1) → f, J_1, face15, face16, edge19, edgeEH, edge17, edge21, edge20, edge23, edge25, edge24, K_1, edge18, edge26, edge22, edge27, L_1, M_1, N_1, face11, face14, face12, face13
  15. Point(Circle[M, Distance[I_1, M], Segment[I_1, M]]) → O_1
  16. Cube(I_1, M, O_1) → g, P_1, face21, face22, edge31, edge28, edge29, edge33, edge32, edge35, edge37, edge36, Q_1, edge30, edge38, edge34, edge39, R_1, S_1, T_1, face17, face20, face18, face19
  17. Point(Circle[S, Distance[M, S], Segment[M, S]]) → U_1
  18. Cube(M, S, U_1) → h, V_1, face27, face28, edge40, edgeMS, edge42, edge44, edge41, edge46, edge48, edge47, W_1, edge43, edge49, edge45, edge50, Z_1, A_2, B_2, face23, face25, face24, face26
  19. Intersect(edge26, zAxis) → C_2
  20. Point(Circle[M_1, Distance[L_1, M_1], Segment[L_1, M_1]]) → D_2
  21. Cube(L_1, M_1, D_2) → i, E_2, face33, face34, edge52, edge51, edge54, edge56, edge53, edge58, edge60, edge59, F_2, edge55, edge61, edge57, edge62, G_2, H_2, I_2, face29, face31, face30, face32