p r o v e space t h a t space t h e space a r e a space o f space s e c t o r space w i t h space s e c t o r space a n g l e space theta space a n d space r a d i u s space r space i s space 1 half r squared theta

Asked by Olivia Adhikary | 4th Aug, 2014, 12:48: PM

Expert Answer:

A r e a space o f space a space c i r c l e space w i t h space r a d i u s space apostrophe r apostrophe space i s space πr squared Angle space subtended space at space centre space in space straight a space circle space is space 360 to the power of straight o space or space 2 straight pi  We space know space that space Area space of space straight a space circlle space and space the space angle space subtended space at space centre space are space directly space proportional. space  therefore space For space an space angle space straight theta space subtended space at space centre space by space straight a space sector comma space Area space of space sector space left parenthesis straight A right parenthesis space is space given space by  πr squared left right arrow space 2 straight pi straight A space left right arrow straight theta  Cross space multiply space and space find space straight A comma space we space get straight A cross times 2 straight pi equals πr squared cross times straight theta straight A equals fraction numerator straight r squared straight theta over denominator 2 end fraction  Hence space Proved

Answered by Dharma Teja | 5th Aug, 2014, 08:29: AM

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