Table-tennis balls packed into a wide-body airliner

Estimate how many ping-pong balls could be packed inside a large passenger jet such as a Boeing 747.

Roughly 15 to 25 million. Treat the pressurised cabin as a cylinder about $60$ m long and $6$ m across, giving roughly $1000\ \text{m}^3$ once seats and fittings are allowed for. A ball is $4$ cm across (about $34\ \text{cm}^3$) and random packing fills about $64\%$ of space, so a cubic metre holds about $19{,}000$ balls, giving around $2\times10^7$. State assumptions clearly and sanity-check the order of magnitude.