Answer
$1.06{\times}{10^{6}}$ $J$
Work Step by Step
A rectangular slice of water $Δx$ $m$ thick and lying $x$ $m$ above the bottom has width $x$ $m$ and volume $8xΔx$ $m^{3}$.
It weighs about $(9.8\times1000)(8xΔx)$ $N$, and must be lifted $(5-x)$ $m$ by the pump, so the work needed is about
$(9.8{\times}{10}^{3})(5-x)(8xΔx)$ $J$
The total work required is
$W$ $\approx$ $\int_0^3(9.8{\times}{10}^{3})(5-x)(8xdx)$ $\approx$ $(9.8{\times}{10}^{3})\left[20x^{2}-\frac{8}{3}{x^{3}}\right]_0^3$ $\approx$ $1.06{\times}{10^{6}}$ $J$
