Question

Find the area of the minor segment of a circle of radius 42cm if length of its corresponding arc is 44

Answer 1

Radius = 42cm

Length of Arc = 2πrtheta/360

44 = 2×22/7×42×theta/360

Theta = 60°

Area of minor segment = πr²theta/360×1/2×r²sintheta.

= 22/7×42×42×60/360×1/2×42×42×sin60° [ sin60°= ✓3/2]

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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 .