Question

A circle has a radius of 63 centimeters. What is the arc length intercepted by a central angle that measures 2π/9 radians? Express the answer in terms of π .

Answer 1

s = 14π cm

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

Answer 2

`\bf \textit{arc's length}\\\\ s=\theta r~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ r=63\\ \theta =(2\pi )/(9) \end{cases}\implies s=\cfrac{2\pi }{9}\cdot 63\implies s=14\pi`