Question

How would I find the length of the highlighted arc in the circle? Also I need to know how I would right the answer using pi as the symbol

Answer 1

The rule of the length of the arc of a circle is

`L=(x^(\circ))/(360^(\circ))*2\pi r`

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

`\begin{gathered} L=(90)/(360)*2*\pi*3 \\ \\ L=(1)/(4)*6\pi \\ \\ L=(6)/(4)\pi \\ \\ L=(3)/(2)\pi \\ \\ L=1.5\pi\text{ unit} \end{gathered}`

The length of the highlight arc is 1.5pi units