14. AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region.

14. AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig. 12.32). If ∠AOB = 30°, find the area of the shaded region.

Solution:

Radius of the larger circle, R = 21 cm

Radius of the smaller circle, r = 7 cm

Angle made by sectors of both concentric circles = 30°

Area of the larger sector = (30°/360°)×πR² cm²

= (1/12)×(22/7)×21² cm²

= 231/2cm²

Area of the smaller circle = (30°/360°)×πr² cm²

= 1/12×22/7×7² cm²

=77/6 cm²

Area of the shaded region = (231/2) – (77/6) cm²

= 616/6 cm² = 308/3cm²