Given:
There are given the value of radius and the value of the angle in radian.
Explanation:
To find the arc length, we need to use the formula of arc length.
So,
From the formula:
[tex]S=r\theta[/tex]
Where,
[tex]\begin{gathered} r=radius \\ \theta=angle\text{ in radians} \end{gathered}[/tex]
So,
Put all the values into the above formula:
Then,
[tex]\begin{gathered} S=r\theta \\ S=6\times\frac{2\pi}{3} \end{gathered}[/tex]
Then,
[tex]\begin{gathered} S=6\times\frac{2\pi}{3} \\ S=2\times2\pi \\ S=4\pi \end{gathered}[/tex]
Final answer:
Hence, the value of arc length is shown below:
[tex]S=4\pi[/tex]
