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单位立方体与体积计算应用

单位立方体与体积计算应用
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2023-03-23 19:43
立体几何几何作图滑块动画
所属专题 Quader und Würfel - Volumen
本范例演示单位立方体（边长为1分米）的体积概念及其在长方体体积计算中的应用。通过GeoGebra的Rotate（旋转）、Segment（线段）、Polygon（多边形）、Sequence（序列）等命令构建三维立方体模型，配合slider（滑块）实现交互式参数调整。重点展示如何通过将长方体分割为若干单位立方体来推导体积公式V=长×宽×高，并提供开放问题让学生计算给定尺寸长方体的体积。适合小学5-6年级学生理解体积概念和空间几何基础知识。

GeoGebra 命令及参数

  1. Rotate(B + ((sliderB_1 * verzerrung), 0), winkel, B) → C
  2. Rotate(A + ((sliderB_1 * verzerrung), 0), winkel, A) → D
  3. Rotate(F + ((sliderB_1 * verzerrung), 0), winkel, F) → G
  4. Rotate(E + ((sliderB_1 * verzerrung), 0), winkel, E) → H
  5. Segment(A, B) → f
  6. Segment(A, E) → g
  7. Segment(F, B) → h
  8. Segment(E, F) → i
  9. Segment(B, C) → j
  10. Segment(A, D) → k
  11. Segment(D, C) → l
  12. Segment(C, G) → m
  13. Segment(G, H) → n
  14. Segment(H, D) → p
  15. Segment(E, H) → q
  16. Segment(F, G) → r
  17. Textfield(aInput) → InputBox1
  18. Polygon(A, B, C, G, H, E) → poly1, a, b, c, g_1, h_1, e
  19. Sequence(Sequence[Polygon[A + (i, cubesVertical - 0.7) + ((j * cubeDepthCathetersWuerfel / 10), (j * cubeDepthCathetersWuerfel / 10)), A + (i, cubesVertical - 0.7) + ((j * cubeDepthCathetersWuerfel / 10), (j * cubeDepthCathetersWuerfel / 10)) + (cubeLengthWuerfel / 10, 0), A + (i, cubesVertical - 0.7) + ((j * cubeDepthCathetersWuerfel / 10), (j * cubeDepthCathetersWuerfel / 10)) + (cubeLengthWuerfel / 10 + cubeDepthCathetersWuerfel / 10, cubeDepthCathetersWuerfel / 10), A + (i, cubesVertical - 0.7) + ((j * cubeDepthCathetersWuerfel / 10), (j * cubeDepthCathetersWuerfel / 10)) + (cubeDepthCathetersWuerfel / 10, cubeDepthCathetersWuerfel / 10)], i, 0, cubesHorizontal - 1, 0.3], j, 0, cubesDepth - 1, 0.3) → cubesAD, {{0.03181980515339422, 0.031819805153394665, 0.031819805153394665, 0.03181980515339422, 0.03181980515339333, 0.03181980515339333, 0.03181980515339422, 0.03181980515339422, 0.031819805153396, 0.031819805153396}}
  20. Sequence(Sequence[Polygon[A + (i, j), A + (i, j) + (cubeLengthWuerfel / 10, 0), A + (i, j) + (cubeLengthWuerfel / 10, cubeLengthWuerfel / 10), A + (i, j) + (0, cubeLengthWuerfel / 10)], i, 0, cubesHorizontal - 1, 0.3], j, 0, cubesVertical - 1, 0.3) → cubesAB, {{0.08999999999999986, 0.08999999999999986, 0.08999999999999986, 0.08999999999999986, 0.08999999999999986, 0.08999999999999986, 0.08999999999999986, 0.08999999999999986, 0.08999999999999986, 0.08999999999999808}}
  21. Sequence(Sequence[Polygon[A + (cubesHorizontal - 0.9, j) + ((i * cubeDepthCathetersWuerfel / 10), (i * cubeDepthCathetersWuerfel / 10)), A + (cubesHorizontal - 0.9, j) + ((i * cubeDepthCathetersWuerfel / 10), (i * cubeDepthCathetersWuerfel / 10)) + (cubeDepthCathetersWuerfel / 10, cubeDepthCathetersWuerfel / 10), A + (cubesHorizontal - 0.9, j) + ((i * cubeDepthCathetersWuerfel / 10), (i * cubeDepthCathetersWuerfel / 10)) + (cubeDepthCathetersWuerfel / 10, cubeDepthCathetersWuerfel / 10 + cubeLengthWuerfel / 10), A + (cubesHorizontal - 0.9, j) + ((i * cubeDepthCathetersWuerfel / 10), (i * cubeDepthCathetersWuerfel / 10)) + (0, cubeLengthWuerfel / 10)], i, 0, cubesDepth - 1, 0.3], j, 0, cubesVertical - 1, 0.3) → cubesBF, {{0.03181980515339333}}
  22. Segment(A_1, B_1) → ab
  23. Segment(A_1, D_1) → ad
  24. Segment(A_1, E_1) → ae
  25. Segment(B_1, F_1) → bf
  26. Segment(B_1, C_1) → bc
  27. Segment(C_1, D_1) → cd
  28. Segment(C_1, G_1) → cg
  29. Segment(D_1, H_1) → dh
  30. Segment(E_1, F_1) → ef
  31. Segment(E_1, H_1) → eh
  32. Segment(F_1, G_1) → fg
  33. Segment(G_1, H_1) → gh
  34. Sequence(Sequence[Polygon[A_1 + (i, j), A_1 + (i, j) + (cubeLengthWuerfel_1 / 10, 0), A_1 + (i, j) + (cubeLengthWuerfel_1 / 10, cubeLengthWuerfel_1 / 10), A_1 + (i, j) + (0, cubeLengthWuerfel_1 / 10)], i, 0, cubesHorizontal_1 - 1], j, 0, cubesVertical_1 - 1) → cubesAB_1, {{1}}
  35. Sequence(Sequence[Polygon[A_1 + (i, cubesVertical_1) + ((j * cubeDepthCathetersWuerfel_1 / 10), (j * cubeDepthCathetersWuerfel_1 / 10)), A_1 + (i, cubesVertical_1) + ((j * cubeDepthCathetersWuerfel_1 / 10), (j * cubeDepthCathetersWuerfel_1 / 10)) + (cubeLengthWuerfel_1 / 10, 0), A_1 + (i, cubesVertical_1) + ((j * cubeDepthCathetersWuerfel_1 / 10), (j * cubeDepthCathetersWuerfel_1 / 10)) + (cubeLengthWuerfel_1 / 10 + cubeDepthCathetersWuerfel_1 / 10, cubeDepthCathetersWuerfel_1 / 10), A_1 + (i, cubesVertical_1) + ((j * cubeDepthCathetersWuerfel_1 / 10), (j * cubeDepthCathetersWuerfel_1 / 10)) + (cubeDepthCathetersWuerfel_1 / 10, cubeDepthCathetersWuerfel_1 / 10)], i, 0, cubesHorizontal_1 - 1], j, 0, cubesDepth_1 - 1) → cubesAD_1, {{0.35355339059327484}}
  36. Sequence(Sequence[Polygon[A_1 + (cubesHorizontal_1, j) + ((i * cubeDepthCathetersWuerfel_1 / 10), (i * cubeDepthCathetersWuerfel_1 / 10)), A_1 + (cubesHorizontal_1, j) + ((i * cubeDepthCathetersWuerfel_1 / 10), (i * cubeDepthCathetersWuerfel_1 / 10)) + (cubeDepthCathetersWuerfel_1 / 10, cubeDepthCathetersWuerfel_1 / 10), A_1 + (cubesHorizontal_1, j) + ((i * cubeDepthCathetersWuerfel_1 / 10), (i * cubeDepthCathetersWuerfel_1 / 10)) + (cubeDepthCathetersWuerfel_1 / 10, cubeDepthCathetersWuerfel_1 / 10 + cubeLengthWuerfel_1 / 10), A_1 + (cubesHorizontal_1, j) + ((i * cubeDepthCathetersWuerfel_1 / 10), (i * cubeDepthCathetersWuerfel_1 / 10)) + (0, cubeLengthWuerfel_1 / 10)], i, 0, cubesDepth_1 - 1], j, 0, cubesVertical_1 - 1) → cubesBF_1, {{0.35355339059327484}}

AI 绘图提示语参考

画一个单位立方体，边长为1分米，并展示如何通过将其分割成小立方体来计算长方体的体积。使用旋转和线段工具构建立方体的三维结构，并添加滑动条来调整参数。通过将长方体分割成单位立方体，展示如何推导出体积公式 V=l×w×h，并为学生提供计算给定尺寸长方体体积的开放性问题。
以上提示语为根据原始绘图命令整理而来，仅供参考。