Find the area of the minor segment of the circle and area of major segment

Описание: A chord of a circle, of radius 14 cm makes an angle of 60 degree at the centre of the circle. Find the area of the minor segment of the circle and area of major segment

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The video explains how to find the area of the minor and major segments of a circle (0:00).

Here's a breakdown of the steps:

Understanding the Problem (0:00-0:39): The problem involves a circle with a radius of 14 cm, where a chord subtends an angle of 60° at the center. The goal is to calculate the area of both the minor and major segments.

Area of Minor Segment Calculation (0:43-4:20):
The formula for the area of a segment is presented as "Area of Sector - Area of Triangle" (0:51-1:09).
The formulas used are (θ/360) * πr² for the sector and (1/2)r²sinθ for the triangle (1:13-1:24).
The values (θ=60°, r=14 cm, π=22/7, sin60°=√3/2) are substituted into the formulas (1:26-1:54).
The calculations involve simplification and approximation of √3 as 1.73 (1:59-2:54).
The final area of the minor segment is approximately 23.67 cm² (3:58-4:20).

Area of Major Segment Calculation (4:22-5:47):
The area of the major segment is found by subtracting the area of the minor segment from the total area of the circle (4:33-4:54).
The area of the circle is calculated using πr² (5:02-5:08).
The minor segment area (23.67 cm²) is subtracted from the circle's area, resulting in approximately 592.33 cm² for the major segment (5:08-5:47).