Applied Hydraulics #$2\mathrm{.}8\mathrm{.}10.$

Figure P$2\mathrm{.}8\mathrm{.}10$ shows a buoy that consists of a wooden pole $25cm$ in diameter and $2m$ long, with a spherical weight at the bottom. The specific gravity of the wood is $0\mathrm{.}62$ and the specific gravity of the bottom weight is $1\mathrm{.}40.$ Determine $($a$)$ how much of the wooden pole is submerged in the water, $($b$)$ the distance to the center of buoyancy from the water level, $($c$)$ the distance to the center of gravity from the water level, and $($d$)$ the metacentric height.

Figure P$2\mathrm{.}8\mathrm{.}10$