Question

Find the area of minor segment of a circle of radius 28 cm, if length of the corresponding arc APB is 44 cm.

Answer 1

Length of an arc =44cm
radius r=28 cm
then, area at the centre =44/pirx180
=44/88x180
=90cm2
Area of minor segment =Area of sector -area of triangle
=1/4pir^2-1/2 Base x height {here base and height are equal }
=3.14x28x28x4-28x28/2
=616-392
=224cm^2
I HOPE THIS WILL HELP YOU....

Answer 2

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 .

Therefore , Area of minor segment is 21 ( 44 - 21 √ 3 ) cm² .