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A target consists of four concentric circles with radii 4 inches, 6 inches, 8 inches and 10 inches as shown. Given that a dart is thrown that hits the target at a random point, what is the probability that it hits a shaded region? Express your answer as a common fraction.

I can't copy the image but basically it is a black circle on the inside with radius of 4, then a white circle around it with a 6 inch radius, then another black circle with 8 inch radius and then finally a white circle of 10 inches.

 Aug 14, 2018
 #1
avatar+98128 
+3

The total area of the target  =  pi * 10^2  = 100 pi in^2

 

One black area is just the black area of a circle with a radius of 4 inches  = pi*4^2   = 16 pi in^2

 

The second black area is the area between the 6 in circle and the 8 in  circle =   the difference in areas of a circle with a radius of 8 in  and a circle with a radius of 6 in  =

pi [ 8^2  - 6^2] = pi [ 64 - 36 ]=    28 pi  in^2

 

So...P(black area)   =  Black Areas / Total Area =  [ 16 + 28 ] pi /  [ 100 pi]  =  44/100  = 11/25

 

 

cool cool cool

 Aug 14, 2018
 #2
avatar+196 
+2

Thanks so much CPhill!!!

 Aug 14, 2018

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