For a saturated soil sample with a void ratio of $1\mathrm{.}400$ and a saturated unit weight of $12\mathrm{.}50k\frac{N}{m^3}.$

Calculate the volume of solids $($in $m^3)$ of the sample if the weight of the solid component is equal to $10$ kN $.$

Note: For your answer, provide only the magnitude accurate to four significant figures. Do not include any units.