The given box has the shape of a <u>cuboid</u>, since its <em>height</em> is greater than its <em>width</em>. Thus, the <em>maximum volume</em> for such box is 11200 .
The <u>volume</u> of an object is a measure of it <em>containing</em> capacity. Since the given box has a taller <em>height</em> than its <em>width</em>, then it has the shape of a <em>cuboid</em>. The<u> volume</u> of a cuboid is given as:
volume = length x width x height
= area x height
Given that the <u>sum</u> of the <em>perimeter</em> of its base and its <em>height</em> is not more than 108 inches, we can say; let the sides of the <em>square</em> base be represented by l and its height by h.
Then;
4l + h = 108
Therefore, maximum volume for the box can be attained when l = 20 inches and h = 28 inches.
So that;
4(20) + 28 = 80 + 28
= 108 inches
Thus;
maximum volume = area of the square base x height
= 400 x 28
maximum volume = 11200
The <u>maximum</u> <u>volume</u> for such a box would be 11200 .