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使用单位立方体测量

使用单位立方体测量
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2022-03-30 16:00
解析几何立体几何几何作图
所属专题 Wiederholung: Flächen- und Raummaße
本范例演示如何使用单位立方体进行体积测量。核心数学概念涉及单位转换和体积计算。通过构造摘要中的GeoGebra命令，学生可以了解如何使用单位立方体进行体积转换。适合5-6年级学生学习测量和体积比较。

GeoGebra 命令及参数

  1. If(step ≟ 5 ∨ step ≟ 6, input ≟ 10, If[step ≟ 8 ∨ step ≟ 9, input ≟ 100, If[step ≟ 11 ∨ step ≟ 12, input ≟ 1000]]) → correct
  2. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {1, 1, 2, 1, 4, 4, 4, 6, 10, 9}
  3. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  4. Textfield(input) → inputBox
  5. Segment(A, B) → ab
  6. Segment(B, C) → bc
  7. Segment(C, D) → cd
  8. Segment(D, A) → ad
  9. Segment(E, F) → ef
  10. Segment(F, G) → fg
  11. Segment(G, H) → gh
  12. Segment(H, E) → eh
  13. Segment(A, E) → ae
  14. Segment(B, F) → bf
  15. Segment(C, G) → cg
  16. Segment(D, H) → dh
  17. Sequence(Sequence[Polygon[A + (i, j), A + (i, j) + (cubeLength / 10, 0), A + (i, j) + (cubeLength / 10, cubeLength / 10), A + (i, j) + (0, cubeLength / 10)], i, 0, cubesHorizontal - 1], j, 0, cubesVertical - 1) → cubesAB, {{1}}
  18. Sequence(Sequence[Polygon[A + (cubesHorizontal, j) + ((i * cubeDepthCatheters / 10), (i * cubeDepthCatheters / 10)), A + (cubesHorizontal, j) + ((i * cubeDepthCatheters / 10), (i * cubeDepthCatheters / 10)) + (cubeDepthCatheters / 10, cubeDepthCatheters / 10), A + (cubesHorizontal, j) + ((i * cubeDepthCatheters / 10), (i * cubeDepthCatheters / 10)) + (cubeDepthCatheters / 10, cubeDepthCatheters / 10 + cubeLength / 10), A + (cubesHorizontal, j) + ((i * cubeDepthCatheters / 10), (i * cubeDepthCatheters / 10)) + (0, cubeLength / 10)], i, 0, cubesDepth - 1], j, 0, cubesVertical - 1) → cubesBF, {{0.35355339059327373}}
  19. Segment(BSmall, CSmall) → bcSmall
  20. Segment(CSmall, DSmall) → cdSmall
  21. Segment(DSmall, ASmall) → adSmall
  22. Segment(ESmall, FSmall) → efSmall
  23. Segment(FSmall, GSmall) → fgSmall
  24. Segment(GSmall, HSmall) → ghSmall
  25. Segment(HSmall, ESmall) → ehSmall
  26. Segment(ASmall, ESmall) → aeSmall
  27. Segment(BSmall, FSmall) → bfSmall
  28. Segment(CSmall, GSmall) → cgSmall
  29. Segment(DSmall, HSmall) → dhSmall
  30. Sequence(Sequence[Polygon[A + (i, cubesVertical) + ((j * cubeDepthCatheters / 10), (j * cubeDepthCatheters / 10)), A + (i, cubesVertical) + ((j * cubeDepthCatheters / 10), (j * cubeDepthCatheters / 10)) + (cubeLength / 10, 0), A + (i, cubesVertical) + ((j * cubeDepthCatheters / 10), (j * cubeDepthCatheters / 10)) + (cubeLength / 10 + cubeDepthCatheters / 10, cubeDepthCatheters / 10), A + (i, cubesVertical) + ((j * cubeDepthCatheters / 10), (j * cubeDepthCatheters / 10)) + (cubeDepthCatheters / 10, cubeDepthCatheters / 10)], i, 0, cubesHorizontal - 1], j, 0, cubesDepth - 1) → cubesAD, {{0.35355339059327373}}
  31. Sequence(Sequence[Polygon[ASmall + (i, j), ASmall + (i, j) + (cubeLength / 10, 0), ASmall + (i, j) + (cubeLength / 10, cubeLength / 10), ASmall + (i, j) + (0, cubeLength / 10)], i, 0, cubesHorizontal - 1], j, 0, cubesVertical - 1) → cubeABSmall, {{1}}
  32. Sequence(Sequence[Polygon[ASmall + (cubesHorizontal, j) + ((i * cubeDepthCatheters / 10), (i * cubeDepthCatheters / 10)), ASmall + (cubesHorizontal, j) + ((i * cubeDepthCatheters / 10), (i * cubeDepthCatheters / 10)) + (cubeDepthCatheters / 10, cubeDepthCatheters / 10), ASmall + (cubesHorizontal, j) + ((i * cubeDepthCatheters / 10), (i * cubeDepthCatheters / 10)) + (cubeDepthCatheters / 10, cubeDepthCatheters / 10 + cubeLength / 10), ASmall + (cubesHorizontal, j) + ((i * cubeDepthCatheters / 10), (i * cubeDepthCatheters / 10)) + (0, cubeLength / 10)], i, 0, cubesDepth - 1], j, 0, cubesVertical - 1) → cubeBFSmall, {{0.35355339059327395}}
  33. Sequence(Sequence[Polygon[ASmall + (i, cubesVertical) + ((j * cubeDepthCatheters / 10), (j * cubeDepthCatheters / 10)), ASmall + (i, cubesVertical) + ((j * cubeDepthCatheters / 10), (j * cubeDepthCatheters / 10)) + (cubeLength / 10, 0), ASmall + (i, cubesVertical) + ((j * cubeDepthCatheters / 10), (j * cubeDepthCatheters / 10)) + (cubeLength / 10 + cubeDepthCatheters / 10, cubeDepthCatheters / 10), ASmall + (i, cubesVertical) + ((j * cubeDepthCatheters / 10), (j * cubeDepthCatheters / 10)) + (cubeDepthCatheters / 10, cubeDepthCatheters / 10)], i, 0, cubesHorizontal - 1], j, 0, cubesDepth - 1) → cubeADSmall, {{0.3535533905932744}}
  34. Segment(meterA, meterB) → meter
  35. Segment(ASmall, BSmall) → abSmall
  36. Segment(BSmall_{1}, CSmall_{1}) → bcSmall_{1}
  37. Segment(CSmall_{1}, DSmall_{1}) → cdSmall_{1}
  38. Segment(DSmall_{1}, ASmall_{1}) → adSmall_{1}
  39. Segment(ESmall_{1}, FSmall_{1}) → efSmall_{1}
  40. Segment(FSmall_{1}, GSmall_{1}) → fgSmall_{1}
  41. Segment(GSmall_{1}, HSmall_{1}) → ghSmall_{1}
  42. Segment(HSmall_{1}, ESmall_{1}) → ehSmall_{1}
  43. Segment(ASmall_{1}, ESmall_{1}) → aeSmall_{1}
  44. Segment(BSmall_{1}, FSmall_{1}) → bfSmall_{1}
  45. Segment(CSmall_{1}, GSmall_{1}) → cgSmall_{1}
  46. Segment(DSmall_{1}, HSmall_{1}) → dhSmall_{1}
  47. Segment(ASmall_{1}, BSmall_{1}) → abSmall_{1}
  48. Segment((-11, 0), (-11.05, 0)) → cubeCM

AI 绘图提示语参考

画一个立方体的体积测量示例，包含多个立方体和测量线。立方体的尺寸可以根据用户输入的值进行调整。示例中包含 3D 立方体、测量线和标签。要求 AI 绘图工具根据用户输入的值生成相应的立方体和测量线，体现出立方体的体积测量过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。