How Many Golf Balls Can Fit in a School Bus

Arne Olav Hallingstad
17th November 2010
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Introduction

I saw an article detailing some of the weird questions asked in job interviews at google. One of the questions was, paraphrashed, how many golf balls could you fit in a school bus. There's obviously no right answer.

Top marks were given for mentioning the Kepler Conjecture. There's an interesting read about the progress towards a proof of the Kepler Conjecture in the past 20 years at that link. It all seemed too interesting to not take a shot at an estimate.

Estimating

There's lots of factors that affects the estimate:

The bus could be short or long
The bus could have a flat floor or have less height in the back to make room for the engine
The seats take up space, but difficult to know how much
Space reserved for the wheels might affect the volume
And more..

To find how many golf balls we can fit in a school bus we can simplify the school bus to be a box of a certain volume, ignoring seats and the varying heights. Let's say the school bus is 3 meters wide. It should have room for a person less than 2 meters to stand up straight. The length is estimated to be about 3 car lengths, where a car might be 5 meters, so 15 meters long.

That gives a total volume of:

	3m * 2m * 15m = 90m^3

That we'll try to pack as efficiently as possible with golf balls.

Now we need to know the volume taken up by a golf ball so we can find how many we can fit in the volume of the bus. Let's say a golf ball has a diameter of 4 cm, that gives a volume of

	(4/3) * PI * r^3
	(4/3) * PI * (2cm)^3 = 1.33 * 3.14 * 8cm^3 = 1.33 * 25cm^3 = 33cm^3 = 0.000033m^3

Looking up the Keppler Conjecture the density is ~74%

	Reduce volume of bus to 75%
	90m^3 - 22.5m^3 = 67.5m^3

	Number of golf balls we can fit in:
	67.5m^3 / 0.000033m^3

Number of golf balls is estimated to 2 045 454.