[tex]\bf \textit{arc's length}\\\\ s=\theta r~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ r=63\\ \theta =\frac{2\pi }{9} \end{cases}\implies s=\cfrac{2\pi }{9}\cdot 63\implies s=14\pi[/tex]
Answer:
s = 14π cm
Step-by-step explanation:
Given:-
- The radius of the circle: r = 63 cm
- The central angle: θ = 2π/9
Find:-
- What is the arc length intercepted by a central angle
Solution:-
- The relationship between the arc length (s) of the circle and the radius of the circle (r) is given by:
s = rθ
- Where, θ is the central angle subtended by the arc length and the radius of the circle. units = rads.
- We will plug θ and r in the formula above and evaluate arc length s.
s = (63)(2π/9)
s = (7)(2π)
s = 14π
- The arc length intercepted by the central angle is s = 14π cm
