Given, length of square sheet of side is $30 \mathrm{~cm}$.



Let, side of small square be $x \mathrm{~cm}$.

Since, a square piece of tin is to be made into a box without top by cutting square from each corner and folding up the flaps to from a box. Then, this shape formed a cuboidal shape.

Thus, volume of the box $(V)$

$$ \begin{aligned} & =(30-2 x)(30-2 x) x \\\\ &\Rightarrow V =x(30-2 x)^2 \end{aligned} $$

On differentiating both side with respect to $x$, we get

$$ \begin{aligned} \frac{d V}{d x} & =(30-2 x)^2+x\{2(30-2 x) \cdot(-2)\} \\\\ & =(30-2 x)^2-4 x(30-2 x) \\\\ & =(30-2 x)\{30-6 x\} \end{aligned} $$

Therefore, maximum of $V, \frac{d V}{d x}=0$

$$ \begin{array}{ll} &\Rightarrow (30-2 x)(30-6 x)=0 \\\\ &\Rightarrow x=15 \text { or } x=5 \quad[x=15 \text { (not taken) }] \end{array} $$

Thus, $x=5$

So, the surface area

$$ \begin{array}{ll} =4 \times(30-2 x) \times x+(30-2 x)^2 & \\\\ =4 \times(30-10) \times 5+(30-10)^2 & (\text { Put } x=5) \\\\ =400+400=800 & \end{array} $$