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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.
Solution
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 .
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