Find the area of the minor segment of a circle of radius 42cm, if length of the corresponding
arc is 44cm.
solve this with area of segment formula only
Answers
radius is 42 cm and length of archana is 44cm and we will take out the value of angle from length of arc
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 .