Answer:
[tex] \displaystyle 38 cm[/tex]
Step-by-step explanation:
We want to find the are length of an arc with a central angle of 2π/3 and a radius of 18cm
Remember the formula of arc length
[tex] \displaystyle l_{ \text{arc}} = \theta r [/tex]
Where:
- r is the radius
- [tex] \theta[/tex] is in radian
Here,
- [tex] \theta \implies 2π/3[/tex]
- r ⇒ 18cm
Now substitute the value of [tex] \theta[/tex] and r into that formula and simplify.
[tex] \displaystyle l_{ \text{arc}} = \frac{2}{3}\pi\cdot 18\\ \implies l_{ \text{arc}}=12\pi\\ \implies l_{ \text{arc}} \approx \boxed{ 38}[/tex]
NB: It should be (2/3)π not 23π
