Question

will this cube - shaped freezer fit through a door that is 5 feet wide? why or why not? (v = 216 ft³)
it depends on the height of the door.
yes, it will fit easily through the door.
only if the freezer is tilted diagonally.
no, it will not fit through the door that is 5 ft.

Explanation:

Step1: Find side - length of cube

The volume formula of a cube is $V = s^{3}$, where $s$ is the side - length. Given $V = 216\ ft^{3}$, then $s=\sqrt[3]{V}=\sqrt[3]{216}=6\ ft$.

Step2: Compare side - length with door width

The side - length of the cube ($6\ ft$) is greater than the width of the door ($5\ ft$). But if tilted diagonally, the diagonal of a square face of the cube can be considered. The diagonal of a square with side - length $s$ is $d = s\sqrt{2}=6\sqrt{2}\approx 6\times1.414 = 8.484\ ft$ (for whole - cube diagonal calculations are more complex, but face - diagonal gives an idea). However, the key is that the side - length is the minimum dimension to consider for non - tilted passage. Since the side - length of the cube ($6\ ft$) is greater than the door width ($5\ ft$), it won't fit without tilting.

Answer:

Only if the freezer is tilted diagonally.