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圆的扇形面积和周长计算练习

圆的扇形面积和周长计算练习
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2024-12-12 23:05
所属专题 Kreis Umfang und Flächeninhalt
本范例演示如何计算特殊圆扇形的面积和周长，涉及圆的几何性质和扇形公式。核心数学概念包括圆的周长公式C=2πr和扇形面积公式A=(θ/360)πr²。作图要点包括使用GeoGebra的圆和扇形构造命令，如Circle和Sector对象。适合小学7-8年级学生，用于巩固圆的几何知识。

GeoGebra 命令及参数

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {1, 3, 7, 9, 2, 9, 7, 6, 8, 5}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Join({Sequence[Segment[Corner[4] + (pixMat * ((k * stepXY), 0)), Corner[4] + (pixMat * ((k * stepXY), maxY))], k, 0, maxX / stepXY], Sequence[Segment[Corner[4] + (pixMat * (0, (k * stepXY))), Corner[4] + (pixMat * (maxX, (k * stepXY)))], k, 0, maxY / stepXY]}) → Raster
  5. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (pixMat * ((k * stepXY), maxY)), Corner[4] + (pixMat * (((k + 1) * stepXY), maxY))], false, true, 0, -1], k, 0, maxX / stepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (pixMat * (maxX, ((k - 1) * stepXY))), Corner[4] + (pixMat * (maxX, (k * stepXY)))], false, true, 1, 0], k, 1, maxY / stepXY]}) → CapRaster
  6. Sequence(Sequence[Corner[4] + (pixMat * ((k * stepXY), (m * stepXY))), k, 0, maxX / stepXY], m, 0, maxY / stepXY) → PR
  7. Sequence(MP1 + (k * (disMP, 0)), k, 0, 3) → MPList
  8. Sequence(Circle[MPList(k), KreisRadius1], k, 1, 4) → CircleList
  9. Take(CircleList, 2, 4) → KreisRand2
  10. Join({Take[CircleAreaList, 2, 4], {Segment[MPList(2) + (0, KreisRadius1), MPList(2) + (0, (-KreisRadius1))]}}) → CirclePerimeterList
  11. Text("\textsf{r}", PDD011, false, true, 0, 0) → txtDD011
  12. Textfield(input031) → InputBox031
  13. Textfield(input032) → InputBox032
  14. Textfield(input033) → InputBox033
  15. Textfield(input041) → InputBox041
  16. Textfield(input051) → InputBox051
  17. Textfield(input052) → InputBox052
  18. Textfield(input091) → InputBox091
  19. Textfield(input101) → InputBox101
  20. Textfield(input111) → InputBox111
  21. Textfield(input112) → InputBox112
  22. Textfield(input113) → InputBox113
  23. Textfield(input114) → InputBox114
  24. Text("\textsf{\bold{Zieh mich!}}", Midpoint[PDDPark011, PDDPark012] + (0, 0.35), false, true, 0, 1) → txtDD01
  25. Text("\textsf{Halbkreisbogen}", PDD081 + (0, 0.05), false, true, 0, 0) → txtDD081
  26. Text("\textsf{\bold{Zieh mich!}}", PDDPark081 + (0, 0.75), false, true, 0, 1) → txtDD08
  27. Text("\textsf{Halbkreis\vphantom{g}}", PosP021 + (0, 0.05), false, true, 0, 0) → txtDD021
  28. Text("\textsf{Viertelkreis\vphantom{g}}", PosP022 + (0, 0.05), false, true, 0, 0) → txtDD022
  29. Text("\textsf{Achtelkreis\vphantom{g}}", PosP023 + (0, 0.05), false, true, 0, 0) → txtDD023
  30. Text("\textsf{\textcolor{#50c1ce}{\bold{Zieh mich!}}", Midpoint[ParkP021, ParkP023] + (0, heightDD02 + 0.5), false, true, 0, 0) → CapZiehMich02
  31. Textfield(input042) → InputBox042
  32. Textfield(input092) → InputBox092
  33. If(step ≟ 4 ∧ (¬correct041), attemptCount041 ≥ 3 ∧ Defined[input041] ∧ (¬correct041), step ≟ 10, attemptCount101 ≥ 3 ∧ Defined[input101] ∧ (¬correct101), step ≟ 11, attemptCount111 + attemptCount112 + attemptCount113 + attemptCount114 ≥ 4 ∧ (Defined[input111] ∧ (¬correct111) ∨ Defined[input112] ∧ (¬correct112) ∨ Defined[input113] ∧ (¬correct113) ∨ Defined[input114] ∧ (¬correct114)), false, step ≟ 4 ∧ correct041, attemptCount042 ≥ 3 ∧ Defined[input042] ∧ (¬correct042), step ≟ 5, attemptCount051 ≥ 3 ∧ (Defined[input051] ∧ (¬correct051) ∨ Defined[input052] ∧ (¬correct052)), step ≟ 9 ∧ (¬correct091), attemptCount091 ≥ 3 ∧ Defined[input091] ∧ (¬correct091), step ≟ 9 ∧ correct091, attemptCount092 ≥ 3 ∧ Defined[input092] ∧ (¬correct092)) → showBtnShowSolution
  34. Center(Kreis4(1)) → MP10
  35. Text("\textsf{2\:r}", PDD012 + (0, 0.05), false, true, 0, 0) → txtDD012
  36. SelectedIndex(dropdown041) → index041
  37. If(step ≟ 2, correctDD02, step ≟ 9, correct091, step ≟ 10, correct101, step ≟ 1, PDD011 ≟ PDDEnd012 ∧ PDD012 ≟ PDDEnd011, true, step ≟ 3, correct031 ∧ correct032 ∧ correct033, step ≟ 4, correctdd041 ∧ correct042, step ≟ 5, correct051 ∧ correct052, step ≟ 8, PDD081 ≟ PDDEnd081 ∧ PDD082 ≟ PDDEnd082) → clickableBtnNext
  38. If(step ≟ 3, (0.5, -0.4), step ≟ 9 ∧ correct091, (8, 6.5), step ≟ 10, (9.25, 8.25), step ≟ 11, (5.5, 8), (2.18, -0.81), step ≟ 4 ∧ (¬correct041), (10, 7.5), step ≟ 4 ∧ correct041, (6, 2), step ≟ 5, (10.5, 1.75), step ≟ 9 ∧ (¬correct091), (6.25, 8.25)) → PosBtnShowSolution
  39. Text("\textsf{Durchmesser\vphantom{gH}}", PDD082 + (0, 0.05), false, true, 0, 0) → txtDD082
  40. Text("\textsf{2\:r\vphantom{gH}}", MP4 + (0, -0.5), false, true, 1, 0) → txt093
  41. SelectedIndex(dropdown101) → index101