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

Answer:

3/10

Step-by-step explanation:

The central angle of the arc is $\frac{3 \pi}{5}$.

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

$C_a = \frac{\theta}{2 \pi} * C$

where C= circumference of the circle

θ = central angle of the arc

Therefore, the circumference of the arc is:

$C_a = \frac{\frac{3 \pi}{5} }{2 \pi} * C\\\\C_a = \frac{3 \pi}{10 \pi} * C\\\\C_a = \frac{3}{10}C$

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