find the area of minor segment of a circle of radius 42cm if length of corresponding arc is 44cm
Answers
42×44=1848 the are of minor srgment of a circle of radius is 1848
Answer:
Given :
Radius r = 42 cm
We have :
Length of arc = 44 cm .
i.e. π r Ф / 180 = 44
Ф = 44 × 180 × 7 / 22 × 42
Ф = 2 × 180 / 6
Ф = 2 × 30
Ф = 60 .
Now :
Area of minor segment = Area of sector - Area of corresponding triangle .
Area of minor segment = π r² Ф / 360 - √ 3 / 4 r²
Area of minor segment = r² ( π Ф / 360 - √ 3 / 4 )
Area of minor segment = 42² ( 22 / 7 × 60 / 360 - √ 3 / 4 )
Area of minor segment = 42² ( 22 / 7 × 1 / 6 - √ 3 / 4 )
Area of minor segment = 42² ( 11 / 7 × 1 / 3 - √ 3 / 4 )
Area of minor segment = 42² ( 11 / 21 - √ 3 / 4 )
Area of minor segment = 42² ( 44 - 21 √ 3 / 84 )
Area of minor segment = 42 × 42 ( 44 - 21 √ 3 / 84 )
Area of minor segment = 42 ( 44 - 21 √ 3 / 2 )
Area of minor segment = 21 ( 44 - 21 √ 3 ) cm² .