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To obtain the area of a sector, what fraction is multiplied by the area of a circle (A = πr2)?

User Bhau
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Let r be a radius of a given circle and α be an angle, that corresponds to a sector.

The circle area is
A=\pi r^2 and denote the sector area as
A_1.
Then
(A_1)/(A)= (\alpha)/(2\pi) (the ratio between area is the same as the ratio between coresponding angles).


A_1=(\alpha)/(2\pi) \cdot A=(\alpha)/(2\pi) \cdot \pi r^2= (r^2\alpha)/(2).

User IChido
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