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

Find the length of the arc shown in red. Leave your answer in term of pie.-example-1
User TompaLompa
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1 Answer

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


\text{ Length of arc = }2\Pi r((\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((\theta)/(360)) \\ \text{Length of red arc = }2\Pi(18)((330)/(360)) \\ \text{Length of red arc = }2\Pi(18)((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

User Den Gas
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