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组合体体积练习：棱柱与棱锥的复合图形

组合体体积练习：棱柱与棱锥的复合图形
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2020-07-16 01:08
多边形立体几何几何作图滑块动画
① 本范例演示如何计算由多个棱柱和棱锥组合而成的复合立体图形的体积，通过交互式输入框和随机出题帮助学生反复练习。② 核心数学概念包括立体几何中的体积公式、组合体的分解与求和，以及空间图形的可视化。③ 作图要点：从构造摘要可见，使用了GeoGebra的Textfield（文本输入框）、Prism（棱柱）、Segment（线段）、Polygon（多边形）等命令，创建了多个棱柱（如PrismA1）及其面、边对象，并通过InputBox1和用户输入（usertext, usernum）实现交互，配合TryAnother（换一题）和HowDidIDo（查看解析）按钮。④ 适合初中高年级或高中学生用于巩固组合体体积计算，也可作为教师课堂演示或学生自主练习工具。

GeoGebra 命令及参数

  1. Textfield(usertext) → InputBox1
  2. Prism(A1, B1, C1, D1, E1) → PrismA1, F1, edgeA1B1, edgeB1C1, edgeC1D1, edgeA1D1, edgeA1E1, edgeAB1, edgeBC1, edgeCD1, S1D2line, S1D1line, G1, edgeBC_1, edgeCE1, H1_1, faceA1B1C1D1, S2B1face, S1B2face, faceBCD1C1, faceA1D1CE1, faceABCE1
  3. Prism(F1, G1, I1, E1) → PrismB1, K1, edgeF1I1, edgeE1F1, edgeAG1, edgeBI1, edgeAE1, edgeAB_2, edgeBE1, J1, S1R2face, faceAE1F1G1, faceABI1G1, S1R1face, faceABE1, edgeF1G1, edgeG1I1
  4. Prism(A2, B2, C2, D2, E2) → PrismA2, F2, edgeA2B2, edgeB2C2, edgeC2D2, edgeA2D2, edgeA2E2, edgeAB2, edgeBC2, edgeCD2, edgeAE2, edgeAB_3, G2, edgeBC_2, edgeCE2, H2_1, faceA2B2C2D2, S1B1face, S2B2face, faceBCD2C2, faceA2D2CE2, S2B3face
  5. Prism(G2, H2_1, I2, J2, K2) → PrismB2, L2, edgeG2H2, edgeH2I2, edgeI2J2, S2D1line, edgeG2K2, edgeAH2, edgeBI2, edgeCJ2, edgeAK2, edgeAB_4, M2, edgeBC_3, edgeCK2, N2, faceG2H2I2J2, faceAH2G2K2, faceABI2H2, S2R2face, S2R3face, S2R1face
  6. Prism(A3, B3, C3, D3, E3) → PrismA3, F3, edgeA3B3, edgeB3C3, edgeC3D3, edgeA3D3, edgeA3E3, edgeAB3_1, edgeBC3, edgeCD3, edgeAE3, edgeAB_5, G3, edgeBC_4, edgeCE3, H3, faceA3B3C3D3, faceAB3A3E3, S3R3face, S3R1face, faceA3D3CE3, S3R2face
  7. Prism(J3, B3, F3, I3, K3) → PrismB3, L3, edgeB3J3, edgeB3F3, S3D1line, edgeI3J3, edgeJ3K3, edgeAB3, edgeBF3, edgeCI3, edgeAK3, edgeAB_6, M3, edgeBC_5, edgeCK3, N3, faceB3F3I3J3, faceAB3J3K3, faceABF3B3, S3B1face, S3B2face, S3B3face
  8. Prism(A5, B5, C5, D5, E5) → PrismA5, F5, edgeA5B5, edgeB5C5, edgeC5D5, edgeA5D5, edgeA5E5, edgeAB5, edgeBC5, edgeCD5, edgeAE5, S5D1line, G5, edgeBC_7, edgeCE5, H5, faceA5B5C5D5, S5R2face, S5R1face, faceBCD5C5, faceA5D5CE5, faceABCE5
  9. Prism(I5, J5, K5, L5, M5) → PrismB5, N5, edgeI5J5, edgeJ5K5, edgeK5L5, edgeI5L5, edgeI5M5, edgeAJ5, edgeBK5, edgeCL5, edgeAM5, edgeAB_7, O5, edgeBC_6, edgeCM5, P5, faceI5J5K5L5, S5B2face, S5B1face, faceBCL5K5, faceB5C5, S5B3face
  10. Prism(A4, B4, C4, D4, E4) → PrismA4, F4, edgeA4B4, edgeB4C4, edgeC4D4, edgeA4D4, edgeA4E4, edgeAB4, edgeBC4, edgeCD4, edgeAE4, edgeAB_8, G4, edgeBC_8, edgeCE4, H4, faceA4B4C4D4, S4B8face, S4B7face, faceBCD4C4, faceA4D4CE4, S4G2face
  11. Prism(E4, F4, J4, I4, K4) → PrismB4, L4, edgeE4F4, edgeF4J4, edgeI4J4, edgeE4I4, edgeE4K4, edgeAF4, edgeBJ4, edgeCI4, edgeAK4, edgeAB_{10}, M4, edgeBC_9, edgeCK4_1, N4, faceE4F4J4I4, S4B6face, S4B5face, faceBCI4J4, faceCI4E4K4, faceABCK4
  12. Prism(H4, G4, P4, O4, Q4) → PrismC4, R4, edgeG4H4, edgeG4P4, edgeO4P4, edgeH4O4, edgeH4Q4, edgeAG4, edgeBP4, edgeCO4, edgeAQ4, edgeAB_{11}, S4, edgeBC_{10}, edgeCQ4, T4, faceG4H4O4P4, faceAG4H4Q4, S4B4face, S4G1face, faceCO4H4Q4, faceABCQ4
  13. Prism(Q4, R4, L4, K4, U4) → PrismD4, V4, edgeQ4R4, edgeL4R4, edgeK4L4, edgeK4Q4, edgeQ4U4, edgeAR4, edgeBL4, edgeCK4, edgeAU4, edgeAB, W4, edgeBC, edgeCU4, X4, faceK4L4R4Q4, faceAR4Q4U4, S4B2face, S4B3face, faceCK4Q4U4, S4B1face
  14. Segment(J2, F2) → edgeJF2
  15. Segment(G3, I3) → lineGI3
  16. Segment(S4, M4) → lineSM4
  17. Segment(P4, J4) → linePJ4
  18. Polygon(S4, M4, J4, P4) → S4R1face, s4, m4, j4, p4
  19. Segment(K5, G5) → lineKG5
  20. Segment(J5, F5) → lineJF5
  21. Segment((-2.5, -2, 0), (-2.5, -2, 4)) → S1HeightMarker
  22. Segment((-0.95929, -3.28198, 0), Midpoint[P4, J4]) → S4Arrow1
  23. Segment((-2.5, -2.21887, 1), Midpoint[S4, P4]) → S4Arrow2
  24. Segment((-3.5, -1, 4), (-3.5, -1, 0)) → S5HeightMarker

AI 绘图提示语参考

绘制一个由多个棱柱和棱锥组成的复合几何体，展示其体积计算。包含多个棱柱，每个棱柱由多个面和边构成，棱柱之间通过共享面组合在一起。添加输入框供用户输入答案，以及按钮用于生成新问题或显示解决方案。使用滑块调整某些参数，并标注高度和关键点，以便理解体积计算。
以上提示语为根据原始绘图命令整理而来，仅供参考。