The Cubic Unit cell of a metal (molar mass $=63.55 \mathrm{g}{ \mathrm{mol}}^{-1}$ ) has an edge length of $362\mathrm{pm}$. Its density is $8.92 \mathrm{g}·{\mathrm{cm}}^{-3}$. The type of unit cell is

We know that the formula of density for a unit cell is mathematically given as:

$\text{ Density }=\frac{\mathrm{Z}\times \mathrm{M}}{{\mathrm{a}}^3\times {\mathrm{N}}_{\mathrm{A}}}$

Rearranging the formula and substituting the given values we get:

$\mathrm{Z}=\frac{\mathrm{d}\times {\mathrm{N}}_{\mathrm{A}}\times {\mathrm{a}}^3}{\mathrm{M}}$

$=\frac{8.92\times 6.023\times {10}^{23}\times {\left(362\times {10}^{-10}\right)}^3}{63.55}=4$

Therefore, the correct answer is face centered cell.