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.  

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^∘

${\displaystyle =\left[\frac{\text{60°}}{{\text{360}}^{\circ }}\right]\times \pi {\left(7\right)}^2+\left[\frac{{80}^{\circ }}{{360}^{\circ }}\right]+[\frac{{80}^{\circ }}{{360}^{\circ }}\times \pi {\left(7\right)}^2]+[{40}^{\circ }\times \pi {\left(7\right)}^2]}$

${\displaystyle =\pi {\left(7\right)}^2(\frac{{60}^{\circ }}{{360}^{\circ }}+\frac{{80}^{\circ }}{{360}^{\circ }}+\frac{{40}^{\circ }}{{360}^{\circ }})}$

${\displaystyle =\pi {\left(7\right)}^2\left(\frac{1}{2}\right)}$

= 77 cm² 

Hence, the area of the shaded region is 77 cm² .