Question

How would I find the length of the arc in this circle? I need to know how to use Pi to represent the symbol for the explanation.

Answer 1

Step 1. The radius of the circle is:

`r=9`

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:

`\begin{gathered} Total\text{ circumference of a circle:} \\ C=2\pi r \end{gathered}`

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:

`Arc=(2\pi r)/(4)`

Step 3. Substituting the known value of r into our equation for the arc:

`Arc=(2\pi(9))/(4)`

Solving the operations:

`\begin{gathered} Arc=(18\pi)/(4) \\ \downarrow \\ Arc=4.5\pi \end{gathered}`

The length of the arc in terms of pi is:

`4.5\pi`

Answer:

`4.5\pi`