$2$ Short answer $(20$ points,

$($a$)$ Suppose I was into very extreme class demos and decided to get a tub of mercury, which has a density of $=13\mathrm{.}6\frac{g}{c}{m}^3.$ Assuming the depth of the tub is about $d=0\mathrm{.}4m,$ do you think I could stand $($float$)$ in the tub so that my feet do not touch the bottom? You can assume that I am a cylinder with a radius of $R=0\mathrm{.}3m$ and a height of $h=1\mathrm{.}7m.$