Question

In the given figure, three sectors of a circle of radius 7 cm, making angles of 60°, 80° and 40° at the centre are shaded. Find the area of the shaded region. [CBSE 2012]

Answer 1

Area of the shaded region = Area of sector having central angle 60^∘ + Area of sector having central angle 80^∘ + Area of sector having central angle 40^∘
$$\begin{gathered} =\left[\frac{60°}{{360}^{°}}\times \mathrm{\pi }{\left(7\right)}^2\right]+\left[\frac{80°}{{360}^{°}}\times \mathrm{\pi }{\left(7\right)}^2\right]+\left[\frac{40°}{{360}^{°}}\times \mathrm{\pi }{\left(7\right)}^2\right] \\ =\mathrm{\pi }{\left(7\right)}^2\left(\frac{60°}{{360}^{°}}+\frac{80°}{{360}^{°}}+\frac{40°}{{360}^{°}}\right) \\ =\mathrm{\pi }{\left(7\right)}^2\left(\frac{180°}{{360}^{°}}\right) \\ =\frac{22}{7}{\left(7\right)}^2\left(\frac{1}{2}\right) \\ =77{\mathrm{cm}}^2 \end{gathered}$$
Hence, the area of the shaded region is 77 cm².