The central angle of an arc of 6π inches and radius of 9 inches is 2 / 3 π radian
Length of an arc
length of an arc = ∅ / 360 × 2πr
where
- r = radius
- ∅ = central angle
Therefore,
r = 9 inches
∅ = ?
length of arc = 6π
Therefore,
6π = 2π(9)∅ / 360
cross multiply
2160π = 18π∅
divide both sides by 18π
∅ = 2160π / 18π
∅ = 120°
Therefore,
180 degrees = π radian
120 degrees =
angle = 120π / 180
angle = 2 / 3 π radian
learn more on arc here: https://brainly.com/question/1509030
#SPJ5
