## Calculus (3rd Edition)

$94579.5 \ J$
The volume of one layer is equal to $0.64 \Delta y \mathrm{m}^{3}$. The force weight of one layer is equal to $3763.2 \pi \Delta y \ N$ Therefore, the work done against can be computed as: $W=\int_{0}^{4} 3763.2 \pi y \ d y\\=3763.2 \pi \int_{0}^{4} y \ d y\\ =3763.2 \ \pi [\dfrac{y^2}{2}]_0^4 \\=30105.6 \pi \\ \approx 94579.5 \ J$