Final answer:
The arc length for a circle with a radius of 6ft and a central angle of 40 degrees is 2π/3 feet, approximately 2.094 feet.
Step-by-step explanation:
To calculate the arc length of a sector when the radius r is 6ft and the central angle is 40 degrees, we first need to convert the angle from degrees to radians, because the formula for arc length involves radians. One full revolution (360 degrees) corresponds to 2π radians. Therefore, 40 degrees is (40/360)*2π = (π/9) radians.
Using the formula for arc length, which is arc length (As) = radius (r) × angle in radians (θ), we plug in our values:
As = 6ft × (π/9) = 6π/9 = 2π/3 ft.
Thus, the arc length is 2π/3 feet, which is approximately 2.094 feet when rounded to three decimal places.