An open cylindrical drum, with a diameter of $2 \mathrm{ft}$ and a length of $4 \mathrm{ft}$, is turned upside down in the atmosphere and then submerged in a liquid so that it floats partially submerged upside down, with air trapped inside. If the drum weighs $150 \mathrm{lb}_{\mathrm{f}}$, and it floats with $1 \mathrm{ft}$ extending above the surface of the liquid, what is the density of the liquid? How much additional weight must be added to the drum to make it sink to the point where it floats just level with the liquid?