A closed cardboard box is to be designed for packing the

We know the volume of the cylinder: 1/4*pie*4 = pie = 3.14

1. Empty box contain 3 cubic feet implies the volume is 3 < pie.
Therefore, cylinder won't fit , and A is sufficient

2. Total surface area is 14 implies 2xy + 2xz + 2yz = 14
but that's all we have so it's insufficient

Therefore, A.

Something to note perhaps: if the area of the cylinder were smaller than the area of the box, then still, we could not conclude that the cylinder would fit based on volume alone. Why? Because we're interested in putting the whole cylinder into the box, not the pieces of the cylinder. In that case, we would need to know more about the dimensions of the box. But this would make the problem very tricky so I am not surprised that in this question the cylinder has a smaller volume. This way, it automatically eliminates any possibilites of the box being large enough.