Question

In the given figure, O is the centre of the circle. m ( arc PQR) = 60^° OP = 10 cm. Find the area of the shaded region.( \[\pi\]= 3.14, \[\sqrt{3}\]= 1.73) 

Answer 1

Radius of the circle, r = 10 cm
m(arc PQR) = ∠POR = θ = 60º
∴ Area of the shaded region = Area of segment PQR

\[= r^2 \left( \frac{\pi\theta}{360°} - \frac{\sin\theta}{2} \right)\]
\[ = \left( 10 \right)^2 \left( \frac{3 . 14 \times 60°}{360°} - \frac{\sin60°}{2} \right)\]
\[ = 100 \times \left( \frac{3 . 14}{6} - \frac{\sqrt{3}}{4} \right)\]
\[ = \frac{314}{6} - \frac{173}{4} \left( \sqrt{3} = 1 . 73 \right)\]
\[ = 52 . 33 - 43 . 25\] 
\[ = 9 . 08 {cm}^2\]

Thus, the area of the shaded region is 9.08 cm².