A circular badge of radius is designed by cutting off two congruent minor segments…
MATHEMATICS · Multi-part · CBSE · Mathematics · Areas Related to Circles · Areas Related to Circles
Problem
A circular badge of radius 8cm is designed by cutting off two congruent minor segments from a full circular sheet. Each segment is formed by a chord that subtends an angle of 60∘ at the centre, and the two chords are placed symmetrically on opposite sides of the centre.
(i) Find the area of one of the minor segments, giving your answer in terms of π and 3.
(ii) Calculate the total area removed from the original circle.
(iii) Determine the area, in terms of π and 3, of the remaining badge after the two segments have been removed.