Fermi estimate: balls required to pack a room measuring 16 by 16 feet

Estimate how many balls it would take to fill a room that measures 16 feet by 16 feet. Talk through how you structure the estimate, state each assumption as you make it, and finish with a number and a range. ```hint Mind the gaps Round balls cannot fill a space solid. Decide how you will account for the empty space between them, and keep the room and the ball in the same units. ``` ### Clarifying Questions - What kind of ball: a ping pong ball, a tennis ball, a basketball, or a mix of sizes? - Is 16 by 16 feet the floor, and if so, how high is the ceiling? - Is the room empty, and should the balls reach all the way to the ceiling? - Are the balls poured in loosely or stacked by hand, and can they be squeezed? ### What a Strong Answer Covers - Ball type and room height settled with the interviewer, or stated as explicit assumptions, before any arithmetic - An equation linking the room's volume, one ball's volume and the share of the room the balls can actually occupy - A justified allowance for the gaps between spheres - Unit conversions and arithmetic that are correct and easy to follow - A sanity check by a second method, a final range, and how the answer moves with ball size or room height ### Follow-up Questions - If the ball's diameter were 10% larger, roughly how much would your answer change, and why is the effect so large? - How would a door, furniture or a sloped ceiling change your method? - How could you test your packing assumption quickly with everyday objects?