If radius of the circle is double of your small circle then the area of the big circle is dash of the small circle
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In two dimensions the answer is simply: as the radius increases, the area increases by the square of the increasing factor. That's a bit abstract, so let's give some examples. If the radius doubles, that's a factor of 2. The square of 2 is 4, so if the radius doubles the area is multiplied by 4.
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