How many ping-pong balls fill a bedroom?

Question

A ping-pong ball is about 4 cm across. Picture an ordinary bedroom roughly 4 m by 4 m with a 2.5 m ceiling. Solve in your head. Estimate how many ping-pong balls it would take to fill the room. Aim: under 45 seconds.

Accepted Answer

Work in metres. Room volume: 4 	imes 4 	imes 2.5 = 40 	ext{ m}^3. Give each ball its own little cube of side 4 cm = 0.04 m: 0.04^3 = 6.4 	imes 10^{-5} 	ext{ m}^3. Dividing: \frac{40}{6.4 	imes 10^{-5}} \approx 6.25 	imes 10^{5} \approx 625{,}000. The cube-per-ball picture leaves no gaps, so it slightly undercounts; real random packing of spheres squeezes in a bit more, pushing the true figure toward 700{,}000–800{,}000. Call it roughly three-quarters of a million balls (range 0.5–0.8 million). Takeaway. For "how many spheres fill a space" always take total volume divided by the cube ar…

How many ping-pong balls fill a bedroom?

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