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Question

Concentric circles of radius 1,2,3,,100 units are drawn such that the interior of the smallest circle is coloured red and the angular regions are coloured alternatively green and red, so that no two adjacent regions are of the same colour. Then the area of green region (in sq. units) is

A
5000 π
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B
5050 π
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C
4950 π
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D
4900 π
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Solution

The correct option is B 5050 π

Area of all the green region =π[(2212)+(4232)++(1002992)]
=π[(2+1)(21)+(4+3)(43)+(6+5)(65)++(100+99)(10099)]
=π[3+7+11++199]
=π[502(3+199)]
=5050 π

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