Question

In the given figure, PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm with centre O. If ∠POQ = 30°, find the area of the shaded region.

Answer 1

Area of the shaded portion = Area of sector OPQ − Area of sector OAB

`= 30^circ/360xxpi(7)^2 - 30^circ/360^circxxpi(3.5)^2`

`=22/7xx1/12[(7)^3 - (3.5)^2]`

`= 22/7 xx 1/12[(7)^2-(7/2)^2]`

`=22/7xx1/12xx147/4`

`=77/8  "cm"^2`

Hence, the area of the shaded portion is`77/8` cm² .