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The dartboard above is made up of three concentric circles with radii 1, 3, and 5. Assuming that a dart thrown will land randomly on the dartboard, what is the probability that it lands in the green region?

 

 Dec 2, 2019
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Red area = pi x r^2 = pi (1^2) = pi

Green area = pi r^2  - the red area = 9 pi - pi = 8 pi

Blue area = pi r^2 - green - red areas = 25pi - 8pi - pi = 16 pi

 

Total area is   pi r^2 = 25 pi                        (16pi + 8pi + pi)

 

green area is 8 pi

   8pi/25pi = 8/25

 Dec 3, 2019

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