find the length of an arc of a circle whose central angle is 4 radians and its diameter is 30 ft
First, we need to find the radius of the circle, which is half of the diameter:
r = 30 ft / 2 = 15 ft
The formula for the length of an arc is:
L = rθ
where L is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.
Substituting the given values:
L = 15 ft × 4 radians = 60 ft
Therefore, the length of the arc is 60 ft.