The figure below shows an annular ring with outer and inner as b and a, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum n number of circles can be painted, then the unpainted area available in annular space is _________ .
Explanation: Area of 1 blue circle,
Hence, area of n blue circles,
Now, Area of annular ring
= πb2 – πa2
Now, answer is, Unpainted area:
= (Area of annular ring) – (Area of n blue color circles) = ( πb2 – πa2 ) - ( nπ((b-a)/2)2 ) = π( b2 – a2 ) - π( (n/4)(b-a)2 ) = π[(b2−a2)−(n/4)(b−a)2]
Option (A) is correct.
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