Answer :
The volume of the box is [tex]4576 in^3.[/tex]
The formula for the volume of a rectangular prism is V = lwh, where l and w are the length and width of the base, and h is the height of the prism. In this case, the base is a square, so l and w are equal. Since the base has an area , we can solve for l and w.
We can use the formula for the area of a square, [tex]A = s^2[/tex], to solve for s, the length of one side of the base. [tex]A = 176 in^2, so s^2 = 176 in^2[/tex], so s = sqrt(176) in.
Now that we have s, we can calculate l and w. l = w = sqrt(176) in.
Now that we have the dimensions of the box, we can calculate the volume. [tex]V = lwh = (sqrt(176))^2 * 26 in^3 = 4576 in^3[/tex].
Therefore, the volume of the box is [tex]4576 in^3.[/tex]
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