Final answer:
To find the radius (r) given the arc length (s = 8.1 ft) and the angle of rotation (θ = π/3 rad), use the formula s = rθ and rearrange to solve for r, giving r ≈ 7.734 ft.
Step-by-step explanation:
The formula for the arc length (s) of a circle when a radius (r) is rotated through an angle θ (in radians) is given by s = rθ. For full credit, we want to find the radius given the arc length s = 8.1 ft and the angle θ = π/3 rad.
To find r, we rearrange the formula to solve for r:
r = s/θ
Now plug in the values:
r = 8.1 ft / (π/3 rad)
r = 8.1 ft / (3.14159.../3)
r ≈ 8.1 ft / 1.04719755
r ≈ 7.734 ft
Therefore, the radius of the circular path is approximately 7.734 feet.