GATE Computer Science (CS) 2020 Solved Papers

Question : 1 of 65

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The figure below shows an annular ring with outer and inner radii as b and a, respect. The annular space has been painted in the form of blue colour circles touching the and inner periphery of annular space. If maximum n number of circles can be painted, then the unpainted area available in annular space is _____

$π[(b^{2}-a^{2})+\;{n}/{4}(b-a)^{2}]$
$π[(b^{2}-a^{2})-\;{n}/{4}(b-a)^{2}]$
$π[(b^{2}-a^{2})-n(b-a)^{2}]$
$π[(b^{2}-a^{2})+n(b-a)^{2}]$

Validate

Solution:

Radius of inner circle

= {a}

Radius of outer circle

= {b}

Radius of small circle

=\;{b-a}/{2}

area of donut shaped figure

=n(b^{2}-a^{2})

Area of each small circle

=π(\;{ {b}- {a}}/{2})^{2}

total area of all small circle

= {n} π(\;{ {b}- {a}}/{2})^{2}

Area of remaining portion

=π(b^{2}-a^{2})-n π(\;{b-a}/{2})^{2}

=π[(b^{2}-a^{2})-\;{n}/{4}(b-a)^{2}]

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