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Question
The area of a circle is 25π sq.cm. Find the length of its arc subtending an angle of 144° at the centre. Also find the area of the corresponding sector.
Solution
Let r be the radius of the circle.
Then πr2 = 25π
∴ r2 = 25
∴ r = 5 cm
Also, θ = 144°
= `(144 × π/180)^"c"`
= `(4π^"c")/5`
∴ length of the arc = S = rθ
= `5 × (4π)/5`
= 4π cm
Area of the corresponding sector = `1/2r^2θ`
= `1/2 × (5)^2 × ((4π)/5)`
= 10π sq cm.
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