Discussion

Explanation:

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).

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