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A sector of a circle with radius 8 cm has a central angle of 45°. What is the area of the corresponding segment?

1. (8 π - 16 √ 2) cm²
2. (8 π - 32) cm²
3. (16 π - 32) cm²
4. (16 π - 64) cm²

Correct answer: (8 π - 16 √ 2) cm²

Solution

The area of the sector is c0r²θ/360 = c0×64×45/360 = 8c0 cm². The triangle formed by the two radii has area 1/2 × 8 × 8 × sin 45° = 16√2 cm². So the segment area is 8c0 - 16√2 cm².

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