Consider the side of the square box be $\"\"$ .

The height of the box be $\"\"$ .

The volume of the box is $\"\"$ .

But volume of the box is $\"\"$ cm³.

$\"\"$

The surface area of the square box is $\"\"$ .

$\"\"$

Area of the square box is minimum when its first derivative becomes zero.

Apply derivative on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

Equate $\"\"$ to zero.

$\"\"$

The side of the square base is $\"\"$ .

Substitute $\"\"$ in $\"\"$ .

$\"\"$

The height of the box is $\"\"$ .

The side of the square base is $\"\"$ .

The height of the box is $\"\"$ .