Concentric circles of radii 1,2,3,. . . ...

Concentric circles of radii `1,2,3,. . . . ,100 c m` are drawn. The interior of the smallest circle is colored red and the angular regions are colored alternately green and red, so that no two adjacent regions are of the same color. Then, the total area of the green regions in sq. cm is equal to `1000pi` b. `5050pi` c. `4950pi` d. `5151pi`

1000 `pi`

5050 `pi`

4950 `pi`

5151 `pi`

Text Solution

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The correct Answer is:

Area of green regions
`=pi[r_(2)^(2)-r_(1)^(2))+(r_(4)^(2)-r_(3)^(2))+…+(r_(100)^(2)-r_(99)^(2))]`
`=pi[r_(1)+r_(2)+r_(3)+r_(4)+….+r_(100)](becauser_(2)-r_(1)=r_(4)-r_(3)=..=r_(100)-r_(99)=1)`
`=pi[1+2+3+...+100]`
`=5050pisq.cm`

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