The L.S.A (lateral surface area) of a cube of side $1\mathrm{cm}$ is,

The correct option is B

$4{\mathrm{cm}}^2$

Find the lateral surface area of a cube:

The lateral surface area of the cube is given by,

$$\begin{gathered} \therefore \mathrm{LSA}=4\times {\left(\mathrm{side}\right)}^2 \\ \Rightarrow =4\times {\left(1\right)}^2 \\ \Rightarrow =4{\mathrm{cm}}^2 \end{gathered}$$

Hence, option ( $B$ ) is correct.