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A circle has radius 8 units, and a central angle is drawn in. The length of the arc defined by the central angle is 4π units. Find the area of the sector outlined by this arc.

 May 27, 2020
 #1
avatar+110682 
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A circle has radius 8 units, and a central angle is drawn in. The length of the arc defined by the central angle is 4π units. Find the area of the sector outlined by this arc.

 

The angle must be in radians.

The circumference of a circle is \(2\pi r\) and there are \(2\pi\) radians in a circle.

 

so the arc length will be     \(\frac{\theta}{2\pi}*2\pi r = \theta r\)

 

You are told that    r = 8 and you are given the arc length so set up a simple equation and solve for theta.

 

Now find the area.

 

 

This is a big enough start please no one else add to it unless GM gives a seriously considered response question.

 May 28, 2020
 #2
avatar+110682 
-2

Actually GM, you can outline the rest of the answer and type it in for all to see.  

That would be excellent.  I like to know I am actually teaching someone.

 May 28, 2020

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