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In the diagram, four circles of radius 4 units intersect at the origin. What is the number of square units in the area of the shaded region? Express your answer in terms of pi.

 

Thanks!

 Apr 18, 2018
 #1
avatar+101228 
+1

Look at the diagram, ACG

 

 

 

 

The area between chord BC  and the edge of the top circle can be found as

 

Area of sector ABC  - area of triangle ABC =

 

(1/4)pi (4)^2  - (1/2)(4^2)sin (90°)  =

 

[ 4pi  - 8 ] units^2

 

And due to symmetry.....we would have 8 of these areas....so....the total area of the shaded regions is

 

8 ( 4pi  - 8  )   =

 

[ 32 pi  - 64]  units ^2

 

 

cool cool cool

 Apr 18, 2018
 #2
avatar+1438 
+2

Thanks so much!

AnonymousConfusedGuy  Apr 18, 2018

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