And I thought, that's not ridiculous at all. That's actually quite an interesting question. Not for the most basic answer, that's pretty trivial -- just guesstimate how many basketballs fit along each dimension and multiply -- but to see whether the candidate asks any interesting followup questions. Like "Hexagonal close-pack, face-centered cubic, or just stuffed in randomly?" Or "Should I assume we've removed the furniture first?" Or "Do you want to use inflated basketballs?"
(And because I was overcome by curiosity, Google & Wikipedia tells me that a regulation basketball is about 30" in circumference, or 9.5 inches in diameter, and that FCC and HCP have the same (optimal) density of ~74%, while random packing is more like 50-60%, with a limit of 64%. The More You Know!)
Yeah. This is my brain.