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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?

  1. $3$
  2. $4$
  3. $1$
  4. $2$
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