5. How many basketballs can you fit in this room?

Let's say the room is 12x12x12 feet.
Holding one's hands apart, a basketball is roughly 9 inches in diameter.
The volume is roughly 64 cubic inches.
The question does not require that I stack these basketballs neatly.
The question is how many basketballs can I fit in this room. So if there is prompt to fit as many basketballs as possible, and I can tuck them into one another like tightly fitted bricks, snugly and with slightly less rigidity in stacking, then in a room that is 6 feet x 6 feet with 12 foot ceilings....

To visualize this...
So picture a layer cake where I might have 16x16 basketballs in one layer or 256 basketballs.
Then 15x15 basketballs in the second layer or 225 basketballs.
Every odd layer 256 basketballs.
Every even layer 225 basketballs.
The ability to have 5 layers of each of 10 layers up to the ceiling if tightly stacked so that the apertures created by one layer of basketballs is filled.
256x5
225x5
2405 basketballs

This isn't nearly the same thing as if done live, in front of an interviewer, sweating with anxiety...... and still it's a terrible question testing poise as much as ability to use basic math and common sense. There is one clever answer to be delivered where if one is allowed to deflate each basketball then the number of basketballs that would fit in the room.... but I presume that the question is asked to see if a candidate can evaluate cubic feet and volume and perform basic math in terms of feet and inches.