Question

A chord of a circle of radius 14cm makes a right angle at the centre. Find the areas of the minor and major segments of the circle.

Answer 1

Area of the minor segment = 56 cm²

Area of the major segment = 560 cm²

Step-by-step explanation:

Given radius = 14 cm.

Angle of the sector = 90 degrees.

 Area of the sector =  (θ/360)(πr²)  

  = 90/360 * 22/7 * 14 * 14

  = 22 * 14 * 2/ 12

  = 154 cm²

Area of the triangle = 1/2 * height * base. Here the triangle is right-angled and height and base equal to radius.  

  = 1/2 * 14 * 14

  = 98 cm²

Area of the circle = πr² = 22/7 * 14 * 14 = 616 cm²

Area of the minor segment = 154 - 98 = 56 cm²

Area of the major segment = 616 - 56 = 560 cm²