Question

What is the arc length of an arc with a central angle of 23π radians in a circle with a radius of 18 cm?

Enter your answer to the nearest whole centimeter in the box.

cm

Answer 1

`\displaystyle 38 cm`

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

`\displaystyle l_{ \text{arc}} = \theta r`

Where:

• r is the radius
• 
  `\theta` is in radian

Here,

• 
  `\theta \implies 2π/3`
• r ⇒ 18cm

Now substitute the value of
`\theta` and r into that formula and simplify.

`\displaystyle l_{ \text{arc}} = (2)/(3)\pi\cdot 18\\ \implies l_{ \text{arc}}=12\pi\\ \implies l_{ \text{arc}} \approx \boxed{ 38}`

NB: It should be (2/3)π not 23π