RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 18. Area of Circle, Sector and Segment

Subject: Maths - Class 10th

Q. No. 14 of Exercise 18B

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The radius of a circle with centre O is 7 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of minor and major segments.

Consider the above figure,

From here we can conclude that the portion or the segment below the chord AB is the minor segment and the segment above AB is major segment.

Also we know,

Area of minor segment = Area of sector – Area of ∆AOB eqn1

Now, Area of sector

Where R = radius of the circle and θ = central angle of the sector

Given, R = 7 cm and θ = 90°

Putting these values in the equation 2, we get

Area of sector = 38.5 cm2 eqn3

Area of AOB = 1/2 × base × height

As triangle is isosceles therefore height and base both are 7 cm.

Area of AOB = 1/2×7×7

= 24.5 cm2 eqn4

Putting values of equation 2 and 4 in equation 1 we get

Area of minor segment = 38.5 – 24.5

Area of minor segment = 14 cm2

Area of major segment = πR2 – Area of minor segment eqn5

Put the value of R, and Area of minor segment in equation 5

= π(72) – 14

= 49π - 14

= (22×7) - 14

= 154 - 14

= 140 cm2

Area of minor segment is 14 cm2 and of major segment is 140 cm2.

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