Question

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

Answer 1

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)`.