Answer:
2093pi/90 cm
Explanation:
You want the exact length of the arc subtended by a 182° central angle in a circle of radius 23 cm.
Arc length
The length of an arc of a circle is given by ...
s = rθ
where θ is the central angle in radians.
Application
The radian measure of an angle of 182° is ...
182°(π/180°) = 91π/90 . . . . radians
Then the arc length is ...
s = (23 cm)(91π/90) = 2093π/90 cm