The rule of the length of the arc of a circle is
[tex]L=\frac{x^{\circ}}{360^{\circ}}\times2\pi r[/tex]
Where
x is the central angle subtended by the arc
r is the radius of the circle
From the given figure
The radius is 3 units, then
r = 3
The central angle of the highlight arc is a right angle, then
x = 90 degrees
Substitute them in the rule above
[tex]\begin{gathered} L=\frac{90}{360}\times2\times\pi\times3 \\ \\ L=\frac{1}{4}\times6\pi \\ \\ L=\frac{6}{4}\pi \\ \\ L=\frac{3}{2}\pi \\ \\ L=1.5\pi\text{ unit} \end{gathered}[/tex]
The length of the highlight arc is 1.5pi units
