Answer:
37.9 cm
Step-by-step explanation:
Arc length is:
s = 2πr (θ/360°)
where r is the radius and θ is the arc angle.
40π cm = 2πr (190°/360°)
20 cm = r (190°/360°)
r = 37.9 cm
Answer: the radius of the circle on which the arc sits is 3.8 cm
Step-by-step explanation:
The formula for determining the length of an arc is expressed as
Length of arc = θ/360 × 2πr
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
θ = 190 degrees
Length of arc = 40π centimeters
Therefore,
40π = 190/360 × 2 × π × r
Dividing both sides of the equation by π, it becomes
40 = 380r/360
380r = 40 × 360 = 1440
r = 1440/380
r = 3.8 to the nearest tenth
