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A circular sector has radius 8 cm and subtends a central angle of 45 degrees at the centre. Find the area of the segment cut off by the chord of this sector.

1. (8 pi - 16 sqrt2) cm^2
2. (8 pi - 32) cm^2
3. (16 pi - 32) cm^2
4. (16 pi - 64) cm^2

Correct answer: (8 pi - 16 sqrt2) cm^2

Solution

Sector area = (45/360) x pi x 64 = 8 pi. Triangle area = (1/2) x 8 x 8 x sin45 = 32 x (sqrt2/2) = 16 sqrt2. Segment = 8 pi - 16 sqrt2 cm^2.

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