Step-by-step explanation:
We have,
An arc subtends an angle of [tex]\dfrac{\pi}{2}\ rad[/tex]or 90 degrees.
It is required to find the fraction of the circumference is this arc. The ratio is given by :
[tex]\dfrac{\text{arc length}}{2\pi r}=\dfrac{\text{angle}}{360}\\\\\dfrac{\text{arc length}}{2\pi r}=\dfrac{90}{360}\\\\\dfrac{\text{arc length}}{2\pi r}=\dfrac{1}{4}\\\\\text{arc length}=\dfrac{2\pi r}{4}\\\\\text{arc length}=\dfrac{C}{4}[/tex]
So, the arc length is one fourth of the circumference.
