Question

In the following figure, `hat(PQ)` and `hat(AB)` are two arcs of concentric circles of radii 7 cm and 3·5 cm respectively, with centre O. If ∠POQ = 30°, then find the areas of shaded region.

Answer 1

Area of shaded region = `π[R^2 - r^2] θ/360^circ`

= `22/7 [7^2 - (3.5)^2] 30^circ/360^circ`

= `22/7 (7 + 3.5)(7 - 3.5) xx 1/12`

= `22/7 xx 10.5 xx 3.5 xx 1/12`

= 9.625 cm²