The required maximum volume of the box would be 85184 cube units.
The surface area of a box is the total area of all of the box's faces. For a box with a square base and no top, the surface area is equal to the sum of the areas of the four sides and the bottom.
To find the maximum volume of such a box, we can first find the length of one side of the square base. We can do this by dividing the given surface area by the number of sides of the box.
In this case, the box has 4 sides plus the bottom, so the length of one side is 220 / 5 = 44.
We can now use the length of one side to find the maximum volume of the box. The volume of a box with a square base and no top is equal to the length of one side cubed.
The length of one side is 44, so the maximum volume of the box is :
⇒ 44 × 44 × 44 = 85184.
Therefore, the maximum volume of the box is 85184 cube units.
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