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Question 13
An archery target has three regions formed by three concentric circles as shown in figure. If the diameters of the concentric circles are in the ratio 1:2:3, then find the ratio of the areas of three regions.


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Solution

Let the diameters of concentric circles be k, 2k and 3k.

Radius of concentric are k2,k and 3k2.

Area of inner circle A1=π(k2)2=k2π4

Area of middle region, A2=π(k)2k2π4=3k2π4

[ Area of ring =π(R2r2). Where R is radius of outer ring and r is radius of inner ring]

And area of outer region A3=π(3k2)2πk2

=9πk24πk2=5πk24

Required ratio =A1:A2:A3

=k2π4:3k2π4:5πk24=1:3:5

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