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GATE CSE 2020 Q8: Unpainted area of an annulus filled with touching circles

Question

The figure below shows an annular ring with outer and inner radii as bb and aa, 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 nn number of circles can be painted, then the unpainted area available in annular space is _____.

Two concentric circles of radii a and b; blue circles fill the ring between them, each touching both the inner and outer circle
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Answer: A (official GATE 2020 final answer key)

Concept used: Unpainted area = annulus area minus the total area of the painted circles.

First step: Each circle spans the ring width, so its diameter is b−ab - a and its area is π(b−a)2/4\pi (b - a)^2/4.

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Source: official GATE 2020 CS question paper and final answer key, organised by IIT Delhi. Question paper · Answer key

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