Answer
$\approx 35467.3 \ J$
Work Step by Step
The volume of one layer is equal to:
$0. 09 \pi (4-y)^2 \Delta y \mathrm{m}^{3}$ .
The force of one layer is equal to:
$529.2 \pi (4-y)^2 \Delta y \ N$
Therefore, the work done against can be computed as:
$ W=\int_{0}^{4} 529.2 \pi (4-y)^2 \Delta y \ d y\\=529.2 \pi \int_{0}^{4} (4-y)^2 y \ d y\\ = 529.2 \pi \ \pi [8y^2-\dfrac{ 8 y^3}{3}+\dfrac{y^4}{4}]_0^4 \\=529.2 \pi [\dfrac{64}{3}] \\ \approx 35467.3 \ J$
