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 `/_A O B=30^@`, find the area of the shaded region.

Explanation

Area of the shaded region = Area of sector ABO - Area of sector CDO
Areas of sectors ABO and CDO can be found by using the formula of
Area of a sector of a circle with angle `theta = theta/(360^@) × pir^2`

Here, r is the radius of the circle and `theta` is the degree measure if the angle
For both the sectors ABO and CDO angle, `theta = 30^@` and radii is `21` cm and `7` cm respectively.
Radius of the sector ABO, R = OB = `21` cm
Radius of the sector CDO, r = OD = `7` cm

Area of shaded region = Area of sector ABO - Area of sector CDO
= `theta/(360^@) × piR^2 - theta/(360^@) × pir^2`
= `theta/(360^@) × pi (R^2 - r^2)`= `30^@/(360^@) × 22/7 [(21 cm)^2 - (7 cm)^2]`

= `1/12 × 22/7 × (441 cm^2 - 49 cm^2)`
= `11/42 × 392 cm^2`
= `308/3 cm^2`