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If radii of three concentric circles are related as
$r_{1} (r_{2} + r_{3}) + r_{2} (r_{3} + r_{1}) + r_{3} (r_{1} + r_{2}) = 94,$ $r_{1} r_{2} (r_{1} + r_{2}) + r_{2} r_{3} (r_{2} + r_{3}) + r_{3} r_{1} (r_{3} + r_{1}) = 384$

and then difference of the area of regions $A_{1} a n d A_{2}$ is

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$4 π$

$9 π$

$2 π$

$7 π$

answer is D.

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Detailed Solution

$r_{1} = 5, r_{2} = 4, r_{3} = 3 A_{1} = π ({r_{1}}^{2} - {r_{2}}^{2}) = 9 π A_{2} = π ({r_{2}}^{2} - {r_{3}}^{2}) = 7 π A_{1} - A_{2} = 2 π$

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