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Question

Concentric circles of radii 1,2,3,......,100cm are drawn. The interior of the smallest circle is coloured red and the angular regions are coloured alternately green and red, so that no two adjecent regions are of the same colour. Then find the total area of green regions in sq.cm.

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Solution

Smallest circle is colured Red
Then Area of Green region for 1st two Circles=π×22π×12
=π×1×3
Then Area of next green region =π×42π×32=π(43)(4+3)=7π
and so on
Last green region area =π×1002π×992=π(10099)(100+99)=199π
Total Green area
=π×1×3+π×1×7+π×1×11+...+π×1×199
=π(3+7+11+...+199)
a=3,n=50,d=4
S=(502)(3+199)=50×101
Area of green region =50×101πcm2=5050πcm2=15871.4cm2

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