A chord of a circle of radius 20 cm subtends an angle of 90° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use π = 3.14 and √3 = 1.73)
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Step-by-step explanation:
Given, radius of circle, r = 20 cm
Corresponding angle, θ = 90°
We have to find the area of the corresponding major segment of the circle.
Area of major segment = area of circle - area of minor segment
Area of minor segment = area of sector - r² sinθ/2 cosθ/2
Area of sector = πr²θ/360°
= (3.14)(20)²(90°/360°)
= (3.14)(400)(1/4)
= (3.14)(100)
= 314 cm²
r² sinθ/2 cosθ/2 = (20)² sin(90°/2) cos(90°/2)
= 400 sin45° cos45°
= 400 (1/√2)(1/√2)
= 400/2
= 200 cm²
Area of minor segment = 314 - 200
= 114 cm²
Area of circle = πr²
= (3.14)(20)²
= (3.14)(400)
= 1256 cm²
Area of major segment = 1256 - 114
= 1142 cm²
Therefore, the area of the major segment is 1142 cm²
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