Answer: approximately 40.9 inches
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 = 11π/18
2π = 360 degrees
π = 360/2 = 180
Therefore,
θ = 11 × 180/18 = 110 degrees
Length of arc = 78.6 inches
Therefore,
78.6 = 110/360 × 2 × 3.14 × r
78.6 = 1.919r
r = 78.6/1.918888
r = 40.9 inches