Question

An open box with a square base is to be made out of a given quantity of card board of

area c² square units. Show that the maximum volume of the box is c³/6√3 cubic units.​

Answer 1

Answer:

The area of the square piece is given to be c2 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, l2+4lh=c2, equating the areas.

Also, the volume of the box is thus given by length × breadth × height = l2h

We can write the volume only in terms of l as l2×4lc2−l2=4lc2−l3

Differentiating this w.r.t l and equating it to zero, we get c2−3l2=0

⇒l=3c2

The volume thus becomes 4lc2−l3=3c2×4c2−3c2

=

=63c3

hope it will help u and plz mark me as brainliest