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  • AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see Fig.). 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.). If \angle \textup{AOB} = 30\degree, find the area of the shaded region.

  

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Area of the shaded region is   =   Area of larger sector   -   Area of smaller sector   

=\ \frac{30^{\circ}}{360^{\circ}}\times \pi \times 21^2\ -\ \frac{30^{\circ}}{360^{\circ}}\times \pi \times 7^2

=\ \frac{30^{\circ}}{360^{\circ}}\times \pi \times (21^2\ -\ 7^2)

=\ \frac{308}{3}\ cm^2

Hence area of the shaded region is    \frac{308}{3}\ cm^2.

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Devendra Khairwa

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