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What is the exact area of the major segment of a circle of diameter 14 cm in which the Minor segment subtends a central angle of 5π÷6 radians
Bot GPT 3.5
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To find the area of the major segment of a circle, we first need to find the area of the entire circle and then subtract the area of the minor segment.
Given that the diameter of the circle is 14 cm, the radius (r) of the circle is half of the diameter, so r = 7 cm.
The central angle subtended by the minor segment is 5π÷6 radians, which means the central angle subtended by the major segment is 2π - 5π÷6 = 7π÷6 radians.
The area of the entire circle is πr^2 = π(7)^2 = 49π sq cm.
The area of the minor segment is (5π÷6) / (2π) x 49π = 35/6 sq cm.
Therefore, the area of the major segment is 49π - 35/6 = (294π - 35) / 6 sq cm.
This is approximately equal to 153.69 sq cm.