Dart-throwing Monkeys
A circular dart board has a radius of 9cm, the board is split into 3 regions. The first region is enclosed in a circle centered in the center of the dart board with a radius of 2cm. The second region is in between the circle that defines the first region and another circle also centered at the center of the dart board and with a radius of cm. The third region is the rest of the dart board that is not occupied by the first or second region.
Monica the Monkey throws a dart at the dartboard. The Probability that the dart hits the second Region is . Find the value of .
The answer is 7.
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1 solution
The area of the whole board is 8 1 π . The area of the second region is ( x 2 − 4 ) π . We are given that the probability that the dart hits the second regions is 9 5 , so we have that 8 1 π ( x 2 − 4 ) π = 8 1 x 2 − 4 = 9 5 . Solving for x , we get that the answer is 7 .