Water of density $1000kg/m^3$ is to be lifted from a rectangular swimming pool of cross – sectional area $200m^2$ and stored in a cylindrical vessel of radius $\frac{1}{\sqrt{\pi }}m$ and length $200m$ whose axis is horizontal and $10m$ above the surface of water of the swimming pool. The work done in filling half of the vessel is ${10}^6\left(y+\frac{x}{3\pi \sqrt{\pi }}\right)J$.