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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!

AnonymousConfusedGuy  Apr 18, 2018
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2+0 Answers

 #1
avatar+86528 
+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

CPhill  Apr 18, 2018
 #2
avatar+1024 
+1

Thanks so much!

AnonymousConfusedGuy  Apr 18, 2018

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