How many tennis balls can fit into a shoe box?

625

A ping-pong ball is a 40mm diameter sphere, which has a volume of 33.5 square centimeters (2.04 in^3). If we assume the ping pong balls naturally pack themselves in Hexagonally Closest Packed (HCP) arrangement, then we have 12^3 inches divided by 2.04in^3, times the 74% packing efficiency of HCP, which gives us about 625 ping pong balls.