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估计液体体积的几何作图方法

估计液体体积的几何作图方法
几何画板及绘图内容加载中，请稍等……
2023-07-21 05:22
立体几何几何作图滑块动画
这个范例演示了如何通过几何图形比较来估计液体的体积。核心数学概念包括容量测量、单位换算和图形面积计算。作图要点包括使用随机种子生成不同容器、通过坐标系定位容器位置、利用滑块动画调整水位高度，并计算左右容器的体积差。适合小学四年级到五年级的学生，用于练习测量和比较容量的技能。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.5667820069717638, 0.5372702360699761, 0.7658734164785514, 0.76475872407, 0.8119757948635971, 0.2085176009191327, 0.3307207470976015, 0.9497138595566683, 0.6320454222044253, 0.987923898086277, 0.7546105055317632, 0.03417492309956099, 0.5278396804261639, 0.07130119320017163, 0.29519102474951314, 0.6167261252572416, 0.09593746254341107, 0.11806150323053002, 0.4713898117344821, 0.5280343144142134, 0.8832137762169975, 0.7852138341082334, 0.01606932083740241, 0.9742769457545373, 0.5832497166088634, 0.10555983815676162, 0.4980504917129809, 0.8152991023379861, 0.9052074563911011, 0.9851402129643219, 0.6675769737567979, 0.16252707914799103, 0.6241799229799327, 0.6007947959808361, 0.19440083176693407, 0.19294563400791737, 0.46135104027927754, 0.48294691385224847, 0.3887151466219878, 0.06016292756872125, 0.6325662876991657, 0.7114083385128872, 0.5021415735284804, 0.6017412411309828, 0.3751137813024818, 0.23312441623309718, 0.7289005366915752, 0.4735631004249833, 0.6346560168028653, 0.020338995830202714, 0.436149562284138, 0.5070328470880967, 0.027327081594865292, 0.57565738459327, 0.6572698798762205, 0.6533787683345273, 0.7760250751007627, 0.15692063984518717, 0.32261377067333113, 0.6412268151111596, 0.6148800707961419, 0.389677963496535, 0.2288955187925139, 0.4389578090151696, 0.031766348390019225, 0.7683540804331174, 0.3410158131739219, 0.17213957595577242, 0.7055547059140896, 0.03895693086787466, 0.6086542032499153, 0.508542233767683, 0.6725633457201685, 0.8163563609197352, 0.004447513037666336, 0.7188992410269907, 0.67536753809389, 0.3477873299905826, 0.27099103020704296, 0.47066851964250167, 0.546766936065236, 0.5312923826302182, 0.5002571871454266, 0.24457723043158047, 0.19228539908409378, 0.9833151601296412, 0.3113214223156521, 0.7097007416084596, 0.03609185033552922, 0.5935934033762048, 0.18051721782113217, 0.6822302768117215, 0.8776822048684371, 0.8778719454168454, 0.3723122923528784, 0.2859260929346825, 0.3000504799657121, 0.30976734200148126, 0.4693050270148854, 0.9285317828010913, 0.784404033364324, 0.6023638135432314, 0.595785713096354, 0.2681423414283405, 0.36174102018287185, 0.7578052789654373, 0.101289394927847, 0.546672915086504, 0.24780962202467827, 0.9092718080052997, 0.5084863063274443, 0.3441671416627427, 0.8351071867721247, 0.31428918097386843, 0.4036148211992035, 0.16771259731790658, 0.30365356763724954, 0.8213180728266692, 0.8474551320637492, 0.5621988024710086, 0.5612866355802933, 0.9130053207730568, 0.030575509300190044, 0.6670563054050442, 0.8541792635169546, 0.8693525671169784, 0.718252125202573, 0.5034581274207288, 0.3891653504555753, 0.07236795542399517, 0.37807154686219796, 0.4702434691621038, 0.07128909979580957, 0.5005151180393873, 0.5467691156929511, 0.3140410529381209, 0.8627551952484077, 0.40645839064334116, 0.5823395633110446, 0.48972286013733846, 0.7331585710740672, 0.7052274326681265, 0.7428758408456015, 0.35141188619896496, 0.6255116079045319, 0.2719836183481553, 0.8549494860207889, 0.7017959244865519, 0.7281620162911361, 0.38906975191417253, 0.1016409342658681, 0.40846665354865397, 0.6192090674638756, 0.730959544349886, 0.4835603918384227, 0.34040763988146533, 0.6474767604731672, 0.013096685863675387, 0.19537024838649616, 0.7155963099361199, 0.5924908915599921, 0.8964234137709174, 0.8354268170302055, 0.07196458239707798, 0.2552333463355083, 0.533647348895628, 0.477204620478583, 0.23867956353443956, 0.4217112238919951, 0.5059799864364329, 0.18814850037274822, 0.8028598782580162, 0.42257826396925124, 0.770203972495739, 0.7445191957070743, 0.9084349996482087, 0.18418596841774532, 0.10548640173827514, 0.1296549298156853, 0.9488847927726559, 0.6295172870263321, 0.5373539297311317, 0.13786670477606391, 0.9240620294221678, 0.10146978475667437, 0.3626801745824347, 0.9469177190715692, 0.18320660920678863, 0.2059058457606347, 0.2944100500299319, 0.9087066253284021, 0.12160048759658983, 0.7277768973211005, 0.29805516602787324, 0.3003823099530945, 0.10709243928449337, 0.840454080646846, 0.19374338374251632, 0.6866625877644912, 0.05493864823438348}
  2. Max(0, floor(animateSolnControl) - 2) → animateIndex
  3. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  4. If(IsInteger[countQuestion / 2], minLevel, maxLevel) → waterLevelLeft
  5. If(waterLevelLeft ≟ minLevel, maxLevel, minLevel) → waterLevelRight
  6. Element({50 + (floor((currentRandomSeeds(5) * 10)) * 50), Element[{0.25, 0.5, 0.75}, 1 + floor((currentRandomSeeds(5) * 3))]}, caseNum) → unitVolume
  7. Max(1, animateIndex - waterLevelRight - 1) → animateIndexLeft
  8. Segment(AnchorCyl2 + (cMajor + 1, 0), AnchorCyl2 + (cMajor + 1, displayHeightRight)) → rightHeight
  9. Polygon({AnchorCyl + (cMajor, 0), AnchorCyl + (cMajor, scale), AnchorCyl + ((-cMajor), scale), AnchorCyl + ((-cMajor), 0)}) → waterFillUnit
  10. Sequence((x(AnchorCyl), y(AnchorTubLeft) + 0.3 + (A * scale)), A, 0, numTicks) → tickAnchors
  11. Element({(("\(" * volumeLeft) * "\)~ml"), ((("\(" * volumeLeft) * "\) liter") * If[0 < volumeLeft ≟ 1, "", "s"])}, caseNum) → volumeLeftLatex
  12. Translate(Ellipse[((-sqrt(cMajor^(2) - cMinor^(2))), 0), (sqrt(cMajor^(2) - cMinor^(2)), 0), cMajor], AnchorCyl) → waterBaseLeft
  13. Corner(5) → layoutAppSize
  14. Translate(CurveCartesian[(cMajor * cos(A)), (cMinor * sin(A)), A, pi, (2 * pi)], AnchorCyl) → cylBase
  15. Polygon({AnchorCyl + (cMajor, 0), AnchorCyl + (cMajor, displayHeightLeft), AnchorCyl + ((-cMajor), displayHeightLeft), AnchorCyl + ((-cMajor), 0)}) → waterFillLeft
  16. Translate(waterBaseLeft, (0, cHeight)) → cylTop
  17. Translate(waterBaseLeft, vTrans) → waterBaseRight
  18. Polygon({AnchorCyl2 + (cMajor, 0), AnchorCyl2 + (cMajor, displayHeightRight), AnchorCyl2 + ((-cMajor), displayHeightRight), AnchorCyl2 + ((-cMajor), 0)}) → waterFillRight
  19. Translate(hottubBackgroundLeft, vTrans) → hottubBackgroundRight
  20. Translate(hottubForegroundLeft, vTrans) → hottubForegroundRight
  21. Zip(Segment[A - (beakerOffset, 0), A + (beakerOffset, 0)], A, Take[tickAnchors, 2]) → beakerTicksLeft
  22. Translate(beakerTicksLeft, vTrans) → beakerTicksRight
  23. Zip(Text[(("\text{Container " * A) * "}"), AnchorCyl + (0, (-cMinor) - 0.8) + B, true, true, 0, 0], A, {1, 2}, B, {(0, 0), vTrans}) → beakerLabels
  24. Segment(AnchorCyl + (cMajor + 1, 0), AnchorCyl + (cMajor + 1, If[animateSolnControl > 0, displayHeightLeft, (waterLevelLeft * scale)])) → leftHeight
  25. Element({"ml", "liter"}, caseNum) → unitLatex
  26. Element({50, 0.25}, caseNum) → minEstimate
  27. Translate(waterBaseLeft, (0, (slideHintLeft * scale))) → hintLeftTop
  28. Polygon({AnchorCyl + (cMajor, 0), AnchorCyl + (cMajor, (slideHintLeft * scale)), AnchorCyl + ((-cMajor), (slideHintLeft * scale)), AnchorCyl + ((-cMajor), 0)}) → hintFill
  29. Translate(waterBaseRight, (0, (slideHintRight * scale))) → hintRightTop
  30. Polygon({AnchorCyl2 + (cMajor, 0), AnchorCyl2 + (cMajor, (slideHintRight * scale)), AnchorCyl2 + ((-cMajor), (slideHintRight * scale)), AnchorCyl2 + ((-cMajor), 0)}) → hintFillRight
  31. CurveCartesian(x(AnchorCyl) + (cMajor * cos(A)), y(AnchorCyl) + (cMinor * sin(A)), A, pi, (2 * pi)) → outlineBase
  32. CurveCartesian(x(AnchorCyl) + (cMajor * cos(A)), y(AnchorCyl) + (cMinor * sin(A)) + (waterLevelLeft * scale), A, 0, pi) → outlineBackLeft
  33. CurveCartesian(x(AnchorCyl) + (cMajor * cos(A)), y(AnchorCyl) + (cMinor * sin(A)) + (waterLevelLeft * scale), A, pi, (2 * pi)) → outlineFront
  34. CurveCartesian(x(AnchorCyl2) + (cMajor * cos(A)), y(AnchorCyl2) + (cMinor * sin(A)) + (waterLevelRight * scale), A, 0, pi) → outlineBackRight
  35. CurveCartesian(x(AnchorCyl2) + (cMajor * cos(A)), y(AnchorCyl2) + (cMinor * sin(A)) + (waterLevelRight * scale), A, pi, (2 * pi)) → outlineFrontRight
  36. Translate(waterFillUnit, vSoln) → waterFillAnimate
  37. Translate(waterBaseLeft, Vector[vSoln + (0, scale)]) → animateTop
  38. Translate(waterBaseLeft, vSoln) → animateBase
  39. Translate(waterBaseRight, (0, displayHeightRight)) → waterTopRight
  40. Textfield(studentEstimate) → inputA
  41. Translate(waterBaseLeft, (0, scale)) → unitWaterTop
  42. Translate(waterBaseLeft, (0, displayHeightLeft)) → waterTopLeft
  43. Element({(("\(" * displayVolumeLeft) * "\)~\mbox{\textsf{ml}}"), (((("\(" * displayVolumeLeft) * "\)~\mbox{\textsf{litre") * If[0 < displayVolumeLeft ≟ 1, "", "s"]) * "}}")}, caseNum) → displayVolumeLeftLatex
  44. Text((("\text{" * If[animateSolnControl > 0, displayVolumeLeftLatex, volumeLeftLatex]) * "}"), Midpoint[leftHeight] + (0.2, 0), true, true, 1, 0) → captionLeft
  45. Text((("\text{" * If[animateSolnControl > 0, displayVolumeRightLatex, volumeRightLatex]) * "}"), Midpoint[rightHeight] + (0.2, 0), true, true, 1, 0) → captionRight

AI 绘图提示语参考

绘制两个圆柱形容器，随机生成不同的水位，用滑块调整水位高度，并标注每个容器的容量单位。容器下方绘制刻度线，并显示每个容器的水位体积数值。容器上方绘制水波纹效果，并添加文字标签标识容器。左侧容器水位随滑块变化，右侧容器水位固定，两个容器之间用箭头连接，表示容量对比关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。