Question

An arc has a length of 30pie ft. Find the length of the radius if the central angle measures 225 degrees

Answer 1

We must find the arc of a circle with arc 30pi and 225 degrees.

For this, we can use the equation for the length of a circle which says that:

`C=2\pi r`

Where r is the radius of the circumference, however first we must find the length of the 360-degree arc of the circumference, for we do the following equality:

`(30\pi)/(C)=(225)/(360)`

Now we clear C:

`\begin{gathered} C=(30\pi\cdot360)/(225) \\ C=(10800\pi)/(225) \\ C=48\pi \end{gathered}`

The length of the 360-degree arc of the circumference is 48pi, we replace this in the first equation and solve for the radius

`\begin{gathered} 48\pi=2\pi r \\ r=(48\pi)/(2\pi) \\ r=24 \end{gathered}`

In conclusion, the answer is that the radius measures 24