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)
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