Answer :

Diameters are in the ratio 1:2:3

So, let the diameters of the concentric circles be 2r, 4r and 6r.

∴ Radius of the circles be r, 2r, 3r respectively.

Now, Area of the outermost circle = π (Radius)^{2} = π (3r)^{2} = 9πr^{2}

Area of the middle circle = π (Radius)^{2} = π (2r)^{2} = 4πr^{2}

Area of the innermost circle = π (Radius)^{2} = π (r)^{2} = πr^{2}

Now, Area of the middle region = Area of middle circle – Area of the innermost circle

= 4πr^{2} - πr^{2} = 3πr^{2}

Now, Area of the outer region = Area of outermost circle – Area of the middle circle

= 9πr^{2} - 4πr^{2} = 5πr^{2}

Required ratio = Area of inner circle: Area of the middle region: Area of the outer region

= πr^{2} : 3πr^{2} : 5πr^{2}

⇒ Required Ratio is 1:3:5

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