Question

Find the length of the arc shown in red. Leave your answer in term of pie.

Answer 1

The general expression for the length of the arc of a circle is express as :

$\text{ Length of arc = }2\Pi r(\frac{\theta}{360})$

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

$\begin{gathered} \text{ Length of red arc = }2\Pi r(\frac{\theta}{360}) \\ \text{Length of red arc = }2\Pi(18)(\frac{330}{360}) \\ \text{Length of red arc = }2\Pi(18)(\frac{330}{360}) \\ \text{Length of red arc = }2\Pi(18)(0.9166) \\ \text{Length of red arc = }32.99\Pi \\ \text{Length of the red arc = 33}\Pi\text{ inch} \end{gathered}$

Answer: A) 33 pie inch