Answer
$967,611$ ft-lbs
Work Step by Step
The work done is defined as follows:
$W=(\pi r^2 h)(\rho)(d)$
Thus, we have
$W=\int_{0}^{10}[\pi (100-y^2) dy] (56) (12-y)$
or, $W=\int_{0}^{10}[56 \pi (100-y^2) (12-y) dy$
or, $W=308,000 \pi \approx 967,611$ ft-lbs