In Fig. find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where ∠AOC = 40°. (use π =22/7)

In the given figure

Area of the region ABCD = Area of sector AOC-Area of sector BOD
$equals fraction numerator 40 degree over denominator 360 degree end fraction x 22 over 7 x space 14 space x space 14 minus fraction numerator 40 degree over denominator 360 degree end fraction x 22 over 7 space x space 7 space space x space 7 equals space 1 over 9 x 22 space x 14 space x 2 minus 1 over 9 space x space 22 space x space 7 space x space 1 equals 22 over 9 space x space left parenthesis 28 minus 7 right parenthesis equals 22 over 9 space x space 21 equals 154 over 3 equals 51.33 space c m squared A r e a space o f space c i r c u l a r space r i n g space equals space 22 over 7 x space 14 space x space 14 minus 22 over 7 space x space 7 space space x space 7 equals 22 space x space 14 space x space 2 minus 22 space x space 7 space x 1 equals space 22 space x space left parenthesis 28 minus 7 right parenthesis equals space 22 space x space 21 equals space 462 space c m squared T h e r e f o r e comma space r e q u i r e d space s h a d e d space r e g i o n equals A r e a space o f space c i r c u l a r space r i n g minus A r e a space o f space r e g i o n space A B D C equals space 462 minus 51.33 equals 410.67 space c m squared T h u s comma space t h e space a r e a space o f s h a d e d space r e g i o n space i s space 410.67 space c m squared$

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