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Area and Perimeter of Special Circle Segments

Area and Perimeter of Special Circle Segments
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2024-12-12 23:05
In collections Kreis Umfang und Flächeninhalt
This example demonstrates calculating the area and perimeter of special circle segments, involving geometric properties of circles and formulas for sectors. Key math concepts include the circumference formula C=2πr and the sector area formula A=(θ/360)πr². Construction involves GeoGebra commands like Circle and Sector objects. Suitable for middle school students to reinforce circle geometry.

GeoGebra Commands & Parameters

  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