A closed empty steel cylindrical tank $2$m in diameter $3$m high is to be used as a buoy in fresh water.

$(1)$ What would be the volume of the concrete cube placed inside the tank if the tank would be submerged $2$m into the water? The steel tank weighs $500$kg$.$ Use Sconc. $=2\mathrm{.}4.$

A$.1\mathrm{.}423$ m$^3$

B$.1\mathrm{.}923$ m$^3$

C$.2\mathrm{.}980$ m$^3$

D$.2\mathrm{.}409$ m$^3$

$(2)$ what is the weight of the concrete cube?

A$.65\mathrm{.}654$ kN

B$.43\mathrm{.}235$ kN

C$.56\mathrm{.}733$ kN

D$.34\mathrm{.}631$ kN

$(3)$ what should be the weight of concrete cube inside to completely submerge the buoy?

A$.93\mathrm{.}238$ kN

B$.101\mathrm{.}229$ kN

C$.73\mathrm{.}298$ kN

D$.87\mathrm{.}552$ kN