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Question

The radius of a circle is 7 cm and it forms a sector by rotating through 60. Then, the radius gets doubled and further moves 30 to form another sector. What is the area of the total region covered by the radius? ( Take π= 227)


A

308 cm2

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B

154 cm2

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C

77 cm2

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D

144 cm2

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Solution

The correct option is C

77 cm2


Area of the sector until the radius is doubled = Area of the pink part

= 60360×π×r2 = π×r26
=227×7×7×16
=1546 cm2 ------(1)

Area of the sector made by the doubled radius = Area of orange part

= 227×30360×((2r)2)
=227×14×14×112
=61612 cm2 ------(2)

Adding (1) and (2) we get

The total area covered by the radius =1546+61612
=92412=77 cm2


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