Question

A circle has a radius of 4 inches. Find the length of the arc intercepted by a central angle of 240 degrees.

Answer 1

- The formula for the length of an arc is

`\begin{gathered} L=(\theta)/(360\degree)*2*\pi* r \\ \\ where, \\ r=\text{ radius of the circle} \\ \theta=\text{ The angle subtended at the center of the circle} \end{gathered}`

- We have been given the following parameters:

`\begin{gathered} \theta=240\degree \\ r=4inches \end{gathered}`

- Thus, we can find the length of the arc as follows:

`\begin{gathered} L=(240\degree)/(360\degree)*2*\pi*4 \\ \\ \therefore L=(16)/(3)\pi\approx16.7552inches \end{gathered}`

Final Answer

The length of the arc is 16.7552inches