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 jth sector is twice that of the (j –1)th sector, for j = 2, ..., 7. What the angle, in radians, subtended by the arc of S1 at the centre of the circle?
Answer: A
Let the area of sector S1 be x units.
The area of the sectors S2, S3, S4, S5, S6, S7 will be 2x, 4x, 8x, 16x, 32x and 64x
∴ The total area of 7 sectors = 127x units = (1/8) × total area of circle = (1/8) π
∴ 127x = π/8 units
A circle subtends an angle of 2π at the centre.
Hence, (1/8)th of the circle will subtend an angle of π/4 at the centre.
i.e. area of the seven sectors i.e. 127x will subtend an angle of π/4 at the centre.
Sector S1, whose area is x will subtend an angle of π/(127 × 4) at the centre.
∴The required angle = π/508 radians
Hence, option (a).