Answer: Yes
Step-by-step explanation:
If the side of the cubic box is:
[tex]l^{2}=250 in^{2}[/tex]
The length of each edge of this cube is:
[tex]l=\sqrt{250 in^{2}}[/tex]
[tex]l=15.8 in[/tex]
So, if the shelf that is 18 inches tall and [tex]l=15.8 inches[/tex] the box wil fit on the shelf.
