Answer:

The area of the square piece is given to be c

2

square units.

Since the base is a square, let the length and breadth of the resulting box be l and the height be h.

Therefore, l

2

+4lh=c

2

, equating the areas.

Also, the volume of the box is thus given by length × breadth × height = l

2

h

We can write the volume only in terms of l as l

2

×

4l

c

2

−l

2

=

4

lc

2

−l

3

Differentiating this w.r.t l and equating it to zero, we get c

2

−3l

2

=0

⇒l=

3

c

2

The volume thus becomes

4

lc

2

−l

3

=

3

c

2

×

4

c

2

−

3

c

2

=

3

c

×

6

c

2

=

6

3

c

3