Question

An arc subtends a central angle measuring \dfrac{3\pi}{5} 5 3π ​ start fraction, 3, pi, divided by, 5, end fraction radians. What fraction of the circumference is this arc?

Answer 1

`(3)/(10)`

Explanation:

Length of an arc
`=(\theta)/(2\pi)X 2\pi r=\theta r`

If the central angle of the arc is
`(3\pi)/(5)`

Length of an arc
`=(3\pi r)/(5)`

Therefore:

Ratio of the length of the arc to the circumference

`=(3\pi r)/(5):2\pi r\\=(3\pi r)/(5*2\pi r)\\=(3)/(10)`

Therefore, the arc is
`(3)/(10)` of the circumference is this arc.