If in a circle of radius 5 cm, one of the sectors makes an angle of 120° and the other one makes an angle of 45° at the centre, what is the ratio of their areas?

Area of a sector making an angle θ at the centre = $\frac{\theta }{360°}\times {\mathrm{\pi r}}^2$
Let θ₁ and θ₂ be the angles formed by the two sectors.
∴ θ₁ = 120° and θ₂ = 45°
∴Ratio of their areas

= $\frac{\frac{{\theta }_1}{360°}\times {\mathrm{\pi r}}^2}{\frac{{\theta }_2}{360°}\times {\mathrm{\pi r}}^2}=\frac{{\theta }_1}{{\theta }_2}=\frac{120}{45}=\frac{8}{3}$