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Question

A chord PQ of a circle with radius 6 cm subtends an angle of 60o with the centre of the circle. The area of the minor and the major segment are _____ and _____ respectively.
(Use π=3.14,3=1.73 )


A
3.27 cm2, 113.04 cm2
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B
113.04 cm2, 3.27 cm2
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C
3.27 cm2, 109.77 cm2
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D
109.77 cm2, 3.27 cm2
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Solution

The correct option is C 3.27 cm2, 109.77 cm2
Radius of the circle, r = 6 cm
Let O be the centre and PQ be the chord of the circle.
POQ=θ=60o

Area of the minor segment
= Area of the shaded region
= Area of sector POQ - Area of POQ
=πr2×θ36034×r2

=3.14×62×603601.734×62

=18.8415.57

=3.27 cm2

Now,
Area of the circle
=πr2
=3.14×6×6
=113.04 cm2

Area of the major segment
= Area of the circle − Area of the minor segment
=113.043.27
=109.77 cm2

Thus, the areas of the minor segment and major segment are 3.27 cm2 and 109.77 cm2, respectively.

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