A square tin sheet of side $12$ inches is converted into a box with open top in the following steps – The sheet is placed horizontally. Then, equal sized squares, each of side x inches, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upwards in the shape of a box. If $x$ is an integer, then what value of $x$ maximizes the volume of the box?
- $3$
- $4$
- $1$
- $2$