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A chord of a circle of radius 20 cm subtends an angle of 90° at the centre. Find the area of the corresponding major segment of the circle. (Use π = 3.14)

Solution:

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

✦ Try This: A chord of a circle of radius 10 cm subtends an angle of 60° at the centre. Find the area of the corresponding major segment of the circle. (Use π = 3.14).

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12

NCERT Exemplar Class 10 Maths Exercise 11.4 Sample Problem 1

A chord of a circle of radius 20 cm subtends an angle of 90° at the centre. Find the area of the corresponding major segment of the circle. (Use π = 3.14)

Summary:

A chord of a circle of radius 20 cm subtends an angle of 90° at the centre. The area of the corresponding major segment of the circle is 1142 cm²

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