" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
a)
r - promień = 5 cm
P - pole koła = πr² = π * 5² = 25π cm²
b)
d - średnica = 3,4 dm
P - pole koła = πd²/4 = π * (3,4)²/4 = π * 11,56/4 = 2,89π dm²
c)
l - obwód = 20π = 2πr
r - promień koła = 20π : 2π = 10 cm
P - pole koła = πr² = π * 10² = 100π cm²
zad 2
a)
r - promień = 12 mm
l - obwód = 2πr = 2 * 12 mm * π = 24π mm
b)
d - średnica = 7 cm
l - obwód = πd = 7π cm
c)
P - pole = 36π cm² = πr²
r² = 36π/π = 36
r = √36 = 6 cm
l - obwód = 2πr = 2 * 6 cm * π = 12π cm
zad 3
r - promień = 6 cm
α = 120°
P - pole wycinka = παr²/360° = π * 120° * 6²/360° = 36π/3 = 12π cm²
ł - długość łuku = παr/180° = π * 120° * 6/180° = 4π cm
zad 4
P - pole wycinka = 3π
α = 30°
παr²/360° = 3π
π * 30° * r²/360° = 3π
πr²/12 = 3π
πr² = 36π
r² = 36π/π = 36
r - promień wycinka = √36= 6
zad 5
ł - długość łuku = 2,5π
α = 45°
ł = παr/180° = 2,5π
π * 45° * r/180° = 2,5π
πr/4 = 2,5π
πr = 10π
r - promień wycinka = 10π/π = 10
zad 6
R - promień zewnętrzny = 12 cm
r - promień wewnętrzny = 7 cm
P - pole pierścienia = π(R² - r²) = π(12² - 7²) = π(144 - 49) = 95π cm²
l - obwód zewnętrzny = 2πR = 2 * 12 cm * π = 24π cm
l₁ - obwód wewnętrzny = 2πr = 2 * 7 cm * π = 14π cm
zad 7
D - średnica zewnętrzna = 12 mm
d - średnica wewnętrzna = 6 mm
R - promień zewnętrzny = D : 2 = 12 mm : 2 = 6 mm
r - promień wewnętrzny = d : 2 = 6 mm : 2 = 3 mm
P - pole uszczelki = π(R² - r²) = π(6² - 3²) = π(36 - 9) = 25π mm²
zad 8
r - promień = 5 m
l - obwód jednego okrążenia = 2πr = 2 * 5 * π = 10π m
20 * 10π m = 200π m = 200 * 3,14 = ≈ 628 m przejdzie koń