Step 1. The radius of the circle is:
[tex]r=9[/tex]
Required: Find the length of the arc.
Note: The angle formed by the arc is a right angle of 90°:
Step 2. We will start by remembering the formula to find the circumference or perimeter of a circle:
[tex]\begin{gathered} Total\text{ circumference of a circle:} \\ C=2\pi r \end{gathered}[/tex]
And since here the blue arc covers a 90° angle, it means that it represents one-fourth of a circle. Therefore, the arc is only 1/4 of the circumference:
[tex]Arc=\frac{2\pi r}{4}[/tex]
Step 3. Substituting the known value of r into our equation for the arc:
[tex]Arc=\frac{2\pi(9)}{4}[/tex]
Solving the operations:
[tex]\begin{gathered} Arc=\frac{18\pi}{4} \\ \downarrow \\ Arc=4.5\pi \end{gathered}[/tex]
The length of the arc in terms of pi is:
[tex]4.5\pi[/tex]
Answer:
[tex]4.5\pi[/tex]
