长方体尺寸与表面积计算

长方体尺寸与表面积计算
几何画板及绘图内容加载中,请稍等……
2018-12-15 00:42
①本范例演示长方体的尺寸计算与表面积求解;②涉及核心数学概念:几何图形的维度、表面积公式、线性回归、三角函数;③作图要点:使用 Point, UnicodeToLetter, LaTeX, Polygon, Prism, TableText, Segment 等命令,构建长方体模型并动态展示其体积与表面积;④适合高中数学教学,用于立体几何与函数应用教学。

GeoGebra 命令及参数

  1. Point(Sequence[(i, -50), i, 1.6, 9, 0.2]) → X
  2. UnicodeToLetter(10007) → xmark
  3. UnicodeToLetter(10003) → cmark
  4. LaTeX("\text{Surface \\area of \\prism}") → yLbl
  5. LaTeX("\text{Side Length of Base}") → xLbl
  6. Polygon(BaseAnchor, BaseAnchor2, 4, xOyPlane) → prismBase, g_1, h, i, j, A, B
  7. Prism(prismBase, PrismTop) → prismDisplay, C, edgeBaseAnchor2C, edgeAD, edgeBE, edgeCPrismTop, edgeCD, edgeDE, edgeEPrismTop, D, E, faceBaseAnchorBaseAnchor2CPrismTop, faceABaseAnchor2CD, faceABED, faceBBaseAnchorPrismTopE, faceCDEPrismTop, edgeBaseAnchorPrismTop
  8. TableText({}) → dataDisplay
  9. TableText({{LaTeX["\text{Height = }"], prismHeight}, {LaTeX["\text{Length of Base = }"], Base}, {LaTeX["\text{Surface Area = }"], prismSA}, {"\text{Volume = }", prismVolume}}, "|101 _1000 r") → tblDisplay
  10. LaTeX("\text{\textbf{Question: }Given a square-based prism with a fixed volume, how do changes in the base \\length affect the height and the surface area? What are the dimensions when the surface \\area is a minimum?}") → MainInstruc
  11. LaTeX("\text{\textbf{Instructions: }Move the slider to adjust the side length of the base.}") → SpecInstruc
  12. LaTeX(((MainInstruc * "\\") * SpecInstruc)) → CompleteInstruc
  13. LaTeX(("\text{Base = }" * x(X))) → sliderLbl
  14. Segment((1.6, -50), (8.9, -50)) → mySlider

AI 绘图提示语参考

绘制一个长方体,调整底面边长以观察高度和表面积的变化。首先画出底面,然后构建长方体,显示其高度、底面边长、表面积和体积。最后,添加说明文字,提示用户移动滑块调整底面边长,观察高度和表面积的变化。
以上提示语为根据原始绘图命令整理而来,仅供参考。