Page 38 - Lösung Merkheft

2.9. KREISBOGEN UND KREISAUSSCHNITT

1 90° 1 90°
As = ∙ A → ∙ πr² b = ∙ u → 360° ∙ 2πr
4
4 360°

1 180°
As = ∙ A → ∙ πr² 1 180° ∙ 2πr
2 360° b = ∙ u →
2 360°

3 270°
As = ∙ A → ∙ πr² 3 270° ∙ 2πr
4 360° b = ∙ u → 360°
4

Kreisausschnitt As Kreisbogen b

2
As = 360° ∙ πr b = 180° ∙ πr

r=3 cm  α=58° As=8,3 cm²α=60° b=6,98 mr=2,6 m r=12 mAs=56,5 m²
As=? b=? r=? b=? α=? As=? α=? b=?
360 180 360
2
2
2
As = ∙ πr As = ∙ πr | ∙ b = ∙ πr | ∙ As = ∙ πr | ∙
360° 360° ∙ 180° ∙ 360° ∙

58° ∙ 360 ∙ 180 ∙ 360
2
2
As = ∙ π3 r = |ඥ = =
360° ∙ π ∙ π ² ∙ π
8,3 ∙ 360
As = 4,56 ² r = √ 60 ∙ π 6,98 ∙ 180 56,5 ∙ 360
r = 4,0 = 2,6 ∙ π = 12 ∙ π
2

b = ∙ πr
180° = 153,82° α = 45°
b = ∙ πr
58° 180°
b = ∙ π ∙ 3 b = ∙ πr
180° 60° 180°
b = ∙ π ∙ 4 As = 360° ∙ πr²
b = 3,04 180° 45°
b = ∙ π ∙ 12
b = 4,19 As = 153,82° ∙ π ∙ 2,6² 180°
360°
b = 9,42
As = 9,07 ²

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