Question

In the given figure, three sectors of a circle of radius 7 cm, making angles of 60°, 80° and 40° at the centre are shaded. Find the area of the shaded region.  

Answer 1

Area of the shaded region = Area of sector having central angle 60^∘ + Area of sector having central angle 80^∘ + Area of sector having central angle 40^∘

`=["60°"/"360"^circ]xxpi(7)^2 + [80^circ/360^circ] + [80^circ/360^circ xx pi(7)^2]+[40^circxxpi(7)^2]`

`=pi(7)^2 (60^circ/360^circ + 80^circ/360^circ+40^circ/360^circ)`

`=pi(7)^2(1/2)`

= 77 cm² 

Hence, the area of the shaded region is 77 cm² .