Find the area of the minor segment of a circle of radius 42cm, if leng

1.	Find the area of the minor segment of a circle of radius 42cm, if length of the correspondingarc is 44cm
Answer» Suppose r is the radius of the circle, and say a chord AB subtends an angle ∅ at its center O, then the Length of the corresponding sector,l = r∅. Given r = 42 cm and l = 44 cm => 44 = 42∅ => 22 = 21∅ => ∅ = 22/21 = π/3. Area of the sector so formed is given by A = 1/2r²∅ Area of minor segment is given by = Area of sector - Area of triangle OAB = 1/24242π/3 - 1/24242sin(π/3) =882(π/3 - √3/2) cm² Like my answer if you find it useful!

Find the area of the minor segment of a circle of radius 42cm, if length of the correspondingarc is 44cm

Answer»

Suppose r is the radius of the circle,

and say a chord AB subtends an angle ∅ at its center O, then the

Length of the corresponding sector,l = r∅.

Given r = 42 cm and l = 44 cm

=> 44 = 42∅

=> 22 = 21∅

=> ∅ = 22/21 = π/3.

Area of the sector so formed is given by A = 1/2*r²*∅

Area of minor segment is given by

= Area of sector - Area of triangle OAB

= 1/2*42*42*π/3 - 1/2*42*42*sin(π/3)

=882(π/3 - √3/2) cm²

Like my answer if you find it useful!