The general expression for the length of the arc of a circle is express as :
[tex]\text{ Length of arc = }2\Pi r(\frac{\theta}{360})[/tex]
In the given figure we have to find the arc of red line :
Angle substended by Red arc = 360 - Angle substended by blue arc
Angle susbtended by Red arc = 360 - 30
Angle substended by Red arc = 330 degree
here, diameter = 36 inch
Radius = Diameter/2
Radius = 36/2
Radius = 18 inch
Substitute the value of radius = 18 inch, angle = 330
[tex]\begin{gathered} \text{ Length of red arc = }2\Pi r(\frac{\theta}{360}) \\ \text{Length of red arc = }2\Pi(18)(\frac{330}{360}) \\ \text{Length of red arc = }2\Pi(18)(\frac{330}{360}) \\ \text{Length of red arc = }2\Pi(18)(0.9166) \\ \text{Length of red arc = }32.99\Pi \\ \text{Length of the red arc = 33}\Pi\text{ inch} \end{gathered}[/tex]
Answer: A) 33 pie inch
