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?

of the circumference


S

Answer 1

3/10

Explanation:

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

The circumference of an arc of a circle is given as:

`C_a = (\theta)/(2 \pi) * C`

where C= circumference of the circle

θ = central angle of the arc

Therefore, the circumference of the arc is:

`C_a = ((3 \pi)/(5) )/(2 \pi) * C\\\\C_a = (3 \pi)/(10 \pi) * C\\\\C_a = (3)/(10)C`

The circumference of the arc will be 3/10 of the circumference of the circle.