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A circular garden of radius 10 m is divided into two parts by a straight line fence. Smaller part is the walking area and flowers are planted in the larger part. The fence is at a distance of 6 m from the centre of the garden. What is the walking area in m2? It is given that cos 53°= 35.


A

36m2

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B

44.5m2

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C

12m2

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D

72m2

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Solution

The correct option is B

44.5m2


In ORQ,
102
= OR2 + RQ2
102
= 62 +RQ2
RQ2
= 64
RQ = 8 m
PQ = 2RQ = 16 m [OR is perpendicular bisector of PQ]

Area of ΔOPQ = 12 × Base × Height
= 12 × PQ × OR
= 12 × 16 × 6
= 48 m2

Area of sector OPSQ = POQ360 × π×r2
In ORQ,
cos(ROQ) = adjacent sidehypotenuse
= OROQ
= 610
= 35
cos( ROQ) = 35
It is given that cos(53) = 35.
Hence ROQ = 53

POQ = 2(ROQ) = 106

Area of sector POQS = POQ360 ×π×r2
= 106360 ×π×102 = 92.5 m2

Area of segment PRQS = Area of sector POQS – Area of OPQ = 92.5 – 48 = 44.5 m2


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