Question

An arc of a circle has a central angle of 120 degrees . If the length of the arc is 5pi inches , what is the radius , , of the circle ?

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

central angle = 120°

length of the arc = 5π in

Step 02:

arcs and circles:

radius:

`\begin{gathered} arc\text{ length = }(\theta)/(360\degree)\text{ * 2}\pi\text{ r } \\ \\ 5\pi\text{ in = }(120\degree)/(360\degree)*\text{ 2}\pi r \end{gathered}`
`\frac{360\degree\text{ * 5}\pi}{120\degree *2\pi}\text{= r}`

r = 7.5 in

The answer is:

r = 7.5 in