Answer: 15 π
Explanation:
The formula for determining the circumference of a circle is expressed as
Circumference = 2πr
Looking at the circle,
Diameter = 18 inches
Radius = diameter/2 = 18/2
Radius = 9 inches
Circumference = 2 × 9 × π = 18π
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 = 9 inches
θ = 60 degrees
Length of arc = 60/360 × 2 × π × 9
Length of arc = 3π
The length of the darkened arc is the circumference of the circle - the arc formed by 60 degrees. Therefore,
length of the darkened arc = 18π - 3π = 15π