1. Consider a circle with unit radius. There are 7 adjacent sectors, S1, S2, S3,....., S7 in the circle such that their total area is (1/8)th of the area of the circle. Further, the area of the $$j^{th}$$ sector is twice that of the $$(j-1)^{th}$$ sector, for j=2, ...... 7. What is the angle, in radians, subtended by the arc of S1 at the centre of the circle?
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By: anil on 05 May 2019 02.31 am
Now area of 1st sector = $$pi * r^2 * frac{x}{360}$$ where x - angle subtended at center Now the next sector will have 2x as the angle, and similarly angles will be in GP with ratio = 2. Sum of areas of all 7 sectors = $$frac{127*x* pi * r^2}{360}$$ which is equal to $$frac{pi * r^2}{8}$$ We get x = $$frac{360}{8*127}$$ Now if converted in radians we get x = $$pi/508$$.
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