Question

encuentra la longitud de arco correspondiente al radio y al angulo dado en cada caso

1. r= 2cm; θ=2π rad

r=28m= 5/9πrad


2.r=5m; θ=2πrad

r=6kmθ=5/9πrad

Answer 1

Tenemos.

Radio(r) = 2cm
Ф = 2π                 π = 180°
Ф = 2 * 180°
Ф = 360°

Arco = 2*π*r*Ф/360°
Arco = 2 * 3,14 * 2cm * 360°/360°     Simplificamos el 360°
Arco = 6,28 * 2cm
Arco = 12,56cm

B)
r = 28m
Ф = 5π/9
Ф = 5*180°/9
Ф = 900/9
Ф = 100°

Sector = 2 * 3,14 * 28m * 100°/360°         Simplificamos
Sector = 6,28 * 28m * 10/36
Sector = 1758,4m/36
Sector = 48,84m


C)
Radio(r) = 5m
Ф = 2π
Ф = 2 * 108°
Ф = 360°

Sector = 2 * 3,14 * 5cm * 360°/360°         Simplificamos el 360°
Sector = 6,28 * 5m
Sector = 31,4m

D)
Radio(r) =
6km
Ф = 5π/9 = 100°

Sector = 2 * 3,14 * 6km * 100°/360°       Simplificamos
Sector = 6,28 * 6km * 10/36
Sector = 376,8km/36
Sector = 10,466km