Metallic lustre is explained by

What is the total volume of atoms present in a face-centre cubic unit cell of a metal ($\mathrm{r}$ is the atomic radius)?

If the answer is of type $\mathrm{a}\times {\mathrm{\pi r}}^3$, report the value of $\mathrm{a}$ in the simplest fraction.

A two-dimensional solid pattern formed by two different atoms $\mathrm{X}$ and $\mathrm{Y}$ is shown below. The black and white squares represent atoms $\mathrm{X}$ and $\mathrm{Y}$, respectively. The simplest formula for the compound based on the unit cell from the pattern is