Area of circle=πr²
=314/100*225
=706.5cm²
chord subtends 60 degree
area of minor segment=theta/360*πr² -1/2r²sintheta
=60/360*314/100*225 -1/2*225*√3/2
=314/100*75 -1/2*225*173/200
=235.5 -97.31
=137.69cm²(approx)
area of major segment=area of circle-area of minor segment
=706.5-137.69
=568.81cm²

- Radius of the circle: 15 cm
- Angle subtended at the center: 60 degrees


- Area of the corresponding minor segment
- Area of the corresponding major segment


Let's start by finding the length of the chord using the given angle and radius.
- We know that the angle subtended at the center is 60 degrees.
- The chord divides the circle into two segments, a minor segment and a major segment.
- The angle at the center also subtends the same angle in the minor and major segments.


- We can form an equilateral triangle with the chord as one of its sides.
- In an equilateral triangle, all sides are equal, and each angle is 60 degrees.
- Therefore, the length of the chord is equal to the side length of the equilateral triangle.
- Using the formula for the side length of an equilateral triangle, we can find the length of the chord:
- Side length = (2 * Radius) * sin(angle/2)
- Side length = (2 * 15 cm) * sin(60 degrees/2)
- Side length = 30 cm * sin(30 degrees)
- Side length = 30 cm * 0.5
- Side length = 15 cm


- To find the area of the minor segment, we need to find the area of the corresponding sector and subtract the area of the triangle formed by the chord and the two radii.
- The area of the sector can be found using the formula: (θ/360) * π * r^2, where θ is the angle in degrees and r is the radius.
- Area of the sector = (60 degrees/360 degrees) * 3.14 * (15 cm)^2
- Area of the sector = (1/6) * 3.14 * 225 cm^2
- Area of the sector = 37.5 cm^2
- The area of the triangle can be found using the formula: (1/2) * base * height, where the base is the length of the chord and the height is the distance from the center to the chord.
- Area of the triangle = (1/2) * 15 cm * (√3/2 * 15 cm)
- Area of the triangle = (1/2) * 15 cm * 12.99 cm
- Area of the triangle = 97.425 cm^2
- Therefore, the area of the minor segment is the difference between the area of the sector and the area of the triangle:
- Area of the minor segment = 37.5 cm^2 - 97.425 cm^2
- Area of the minor segment ≈ -59.925 cm^2


- The area of the major segment is the sum of the area of the sector and the area of the triangle formed by the chord and the two radii.