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.

Given:

Radius of inner circle = 3.5 cm

Radius of outer circle = 7 cm

∠POQ = 30°

Let the sector made by the arcs PQ and AB be S_{1} and S_{2} respectively.

Then, Area of shaded region = Area of S_{1} – Area of S_{2} ………….(i)

∵ Area of sector = × πr^{2}

∴ Area of S_{1} = × × 7 × 7

= cm^{2}

Similarly, Area of S_{2} = × × 3.5 × 3.5

= cm^{2}

Thus, using (i), we have

Area of shaded region = -

=

= = cm^{2}

__Hence, the area of shaded region is__ __cm ^{2}.__

30