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

Answer:

$\dfrac{3}{10}$

Step-by-step explanation:

Length of an arc$=\dfrac{\theta}{2\pi}X 2\pi r=\theta r$

If the central angle of the arc is $\dfrac{3\pi}{5}$

Length of an arc$=\dfrac{3\pi r}{5}$

Therefore:

Ratio of the length of the arc to the circumference

$=\dfrac{3\pi r}{5}:2\pi r\\=\dfrac{3\pi r}{5*2\pi r}\\=\dfrac{3}{10}$

Therefore, the arc is $\dfrac{3}{10}$ of the circumference is this arc.