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Annulus (Circle Ring) Circumference & Area: Using r₁²−r₂² Formulas

Annulus (Circle Ring) Circumference & Area: Using r₁²−r₂² Formulas
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2024-12-18 20:44
In collections Kreis Umfang und Flächeninhalt
This GeoGebra example demonstrates how to compute the area and the circumference of an annulus formed by two circles with given radii r1 and r2. Students can practice both the direct formulas and answer multiple-choice questions that select the correct area and perimeter expressions. The key math concepts are the annulus area as the difference of two circle areas, A = π(r1² − r2²), and the annulus

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {8, 2, 8, 7, 3, 2, 9, 10, 5, 4}
  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. Segment(MP01, MP01 + (KreisRadius011, 0)) → segR011
  8. Segment(MP01, MP01 + (0, (-KreisRadius012))) → segR012
  9. Segment(MP091, MP091 + (KreisRadius091, 0)) → segR091
  10. Segment(MP091, MP091 + (0, (-KreisRadius092))) → segR092
  11. Segment(MP092, MP092 + (0, (-KreisRadius092))) → segR094
  12. Segment(MP092, MP092 + (KreisRadius091, 0)) → segR093
  13. SelectedIndex(dropdown031) → index031
  14. SelectedIndex(dropdown032) → index032
  15. SelectedIndex(dropdown071) → index071
  16. If(step ≟ 3, correctdd031 ∧ correctdd032, step ≟ 7, correctdd071, step ≟ 4, PDD041 ≟ PDDEnd042 ∧ PDD042 ≟ PDDEnd041, step ≟ 8, PDD081 ≟ PDDEnd082 ∧ PDD082 ≟ PDDEnd081, true) → clickableBtnNext
  17. Text("\textsf{\bold{Zieh mich!}}", Midpoint[ParkPDD041, ParkPDD042] + (0, -0.5), false, true, 0, -1) → CapDD041
  18. Text("\textsf{\pi}", PDD081 + (0, 0.05), false, true, 0, 0) → txtDD081
  19. Text("\textsf{2\:r_1}", PDD082 + (0, 0.05), false, true, 0, 0) → txtDD082
  20. Text("\textsf{\bold{Zieh mich!}}", Midpoint[ParkPDD081, ParkPDD082] + (0, -0.5), false, true, 0, -1) → CapDD081
  21. Circle(MP01, KreisRadius011) → KreisSchraffierung1
  22. Circle(MP01, KreisRadius012) → KreisSchraffierung2
  23. Text("\textsf{r_2²}", PDD041 + (0, 0.05), false, true, 0, 0) → txtDD041
  24. Text("\textsf{r_1²}", PDD042 + (0, 0.05), false, true, 0, 0) → txtDD042
  25. Circle(MP092, KreisRadius011) → KreisArea093
  26. Circle(MP092, KreisRadius012) → KreisArea094