Two balls float on the surface of a pool filled with fresh water of density $1,000k\frac{g}{m^3}.$ If ball A has $45\%$ of its volume above the surface of the water, and ball B has $55\%$ of its volume above the surface, what is the ratio of the density of ball $A$ to that of ball $B?$

Multiple Choice

$0\mathrm{.}818$

$0\mathrm{.}935$

$1\mathrm{.}07$

$1\mathrm{.}22$