(MATHEMATICS) the arc of a circle of radius 20cm subtend an angle of 120degree at the centre use the value 3.142 for pie to calculate the area of the sector correct to the nearest cmsquared
s = rθ
A = 1/2 r^2 θ = 1/2 (s/θ)^2 θ = s^2/(2θ) = 20^2/(2 * 2π/3) = 300/π cm^2
or, since s = rθ,
r = 20/(2π/3) = 30/π
the angle is 1/3 of a circle, so
A = 1/3 πr^2 = 1/3 π (30/π)^2 = 300/π cm^2