Answer:
27 m
Step-by-step explanation:
To find the diameter of the circle, we use the relationship between the arc length, the central angle, and the circumference of the circle.
Given that the arc length is 9π meters and the central angle is 120°, we use the formula:
[tex]L = \dfrac{\theta}{360} \times 2\pi r[/tex]
We plug in the values we know:
[tex]9\pi = \frac{120}{360} \times 2\pi r[/tex]
Simplify to find the radius r
[tex]r = \frac{9\pi \times 3}{2\pi} = \frac{27}{2} = 13.5 m[/tex]
Since diameter d is twice the radius r,
d = 2r = [tex]2 \times 13.5[/tex] = 27m
