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There are three concentric circles as shown in the figure. The radii of them are $$2\text{ cm}$$, $$4\text{ cm}$$ and $$6\text{ cm}$$. The ratio of the area of the shaded region to the area of the dotted region is $$\frac{a}{b}$$ where $$a, b$$ are integers and have no common factor other than 1. Then $$a + b$$ =
Correct Answer: 8
The shaded ring lies between the circles of radius 2 and 4, with area proportional to $$4^2 - 2^2 = 12$$. The dotted ring lies between the circles of radius 4 and 6, with area proportional to $$6^2 - 4^2 = 20$$. The ratio is $$\frac{12}{20} = \frac{3}{5}$$, so $$a = 3$$, $$b = 5$$, and $$a + b = 8$$.
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