"Area of a Sector" Question (1 Viewer)

[Mc_Meaney]

"The area of a sector is 3pi/10cm^2 and the arc length cut off by the sector is pi/5cm. find the angle subtended at the centre of the circle and find the radius of the circle"

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[word.]

the arc length would be given by 2 * pi * r * angle/2pi = r * angle
then area = pi * r^2 * angle/2pi = 1/2 * angle * r^2

equate and solve simultaneously..
let angle = @
r@ = pi/5 ..(1)
(@r^2)/2 = 3pi/10 ..(2)

(2)-> @r^2 = 3pi/5
@ = 3pi/(5r^2) ->(1)
3pi/(5r) = pi/5,
r = 3cm ->(1)
@ = pi/15

 

[Mc_Meaney]

Thanx mate