AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O. If ∠AOB=30∘, find the area of the shaded region.
Given:
Radius of the larger sector, R=21 cm
Radius of the smaller sector, r=7 cm
Angle subtended by sectors of both concentric circles =30∘
Area of the sector making angle θ
=(θ360∘)×πr2
Area of the larger sector
=(30∘360∘)×πR2cm2
=112×227×212 cm2
=112×227×21×21 cm2
=2312 cm2
Area of the smaller circle
=(30∘360∘)×πr2cm2
=112×227×72 cm2
=112×227×7×7 cm2
=776 cm2
Area of the shaded region = Area of the larger sector − Area of the smaller sector
=(2312−776) cm2
=6166 cm2
=3083 cm2
=10223 cm2