Answer
$141.26 \ k \ J$
Work Step by Step
The force of one layer is equal to:
$\ Force= \ Mass \times \ gravity = 39.24 (1000-100 y) \Delta y \ N$
Therefore, the work done against can be computed as:
$ W=39.24 \int_{0}^{3} (1000-100 y) \times y \ d y\\= 39.24 \int_{0}^{3} (1000y-100y^2) \ d y\\ = 39.24 [\dfrac{1000y^2}{2}-\dfrac{100 y^3}{3} ]_0^{3} $
By using a calculator, the required result is:
$W =141.26 \ k \ J$
