A circular pond has area equal to 616 m². A circular stage is made at the centre of the pond whose radius is equal to half the radius of the pond. What is the area where water is present ?

Solution(By Examveda Team)

Let the radius of the pond be R metres
Then,
$$\eqalign{ & \pi {R^2} = 616 \cr & \Rightarrow {R^2} = \frac{{616 \times 7}}{{22}} \cr & \Rightarrow {R^2} = 196 \cr & \Rightarrow R = 14\,m \cr} $$
Radius of the stage :
$$\eqalign{ & = \left( {\frac{{14}}{2}} \right)m \cr & = 7\,m \cr} $$
∴ Area where water is present :
$$\eqalign{ & = \pi \left( {{{14}^2} - {7^2}} \right){m^2} \cr & = \left( {\frac{{22}}{7} \times 21 \times 7} \right){m^2} \cr & = 462\,{m^2} \cr} $$