Q. 514.6( 9 Votes )

Find the area of the major segment APB of a circle of radius 35 cm and AOB = 90°, as shown in the given figure.


Answer :

Given:

Radius of Circle = 35 cm


AOB = 90°


Area of Sector = × πr2


= × × 35 × 35


= cm2


∆ AOB is right-angled triangle.


Area of ∆ AOB = × OA × OB


= × 35 × 35


= cm2


Now, Area of Minor Segment ACB


= Area of Sector – Area of ∆AOB


= - = = 350 cm2


Area of Circle = πr2


= × 35 × 35


= 22 × 5 × 35


= 3850 cm2


Thus, Area of Major Segment = Area of Circle – Area of Minor Segment = 3850 – 350 = 3500 cm2


Hence, the area of the major segment is 3500 cm2.


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