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In the figure below, O is the center of the circle, and the radius of the circle is 8. Angle BOA is right. What is the area of the filled-in (purple) region?

Explain the steps of your solution. Give your answer in exact form (which may involve pi). In other words, don't round off (but do simplify if you can).

 

 

Guest Nov 9, 2017
 #1
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Since AOB is 90°, the  whole area is just the area of 1/4 of a circle = pi (8)^2 / 4  =

64 pi / 4  =  16 pi  units^2       (1)

 

The area of the triangular part of the figure is(1/2) * 8^2  =  64/2  = 32 units^2     (2)

 

So...the purple area is just   (1)  - (2)  =   [16 pi - 32 ] units^2 

 

 

cool cool cool

CPhill  Nov 9, 2017

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