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.

ColdplayMX
Aug 14, 2018

#1**+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

CPhill
Aug 14, 2018