Final answer:
The length of the arc subtended by a central angle of 60° in a circle with a radius of 3 meters is approximately 3.14 meters. This is found by converting the angle to radians and using the formula for arc length in relation to radius and angle in radians.
Step-by-step explanation:
The length of the arc subtended by a central angle of 60° in a circle with a radius of 3 meters can be found using the formula:
arc length (s) = radius (r) × angle (θ) (in radians).
First, we must convert the central angle from degrees to radians. There are 2π radians in a full circle (360°), so to convert degrees to radians, we use the following calculation:
60° × (π/180°) = π/3 radians.
Now, using this angle in radians, we can calculate the arc length as follows:
s = r × θ = 3 m × (π/3) = 3π/3 m = π meters.
Approximating π as 3.14, we find that:
s ≈ 3.14 meters.
The correct option for the length of the arc is b) 3.14 meters.