# How many ping pong balls would fit into the Great Pyramid?

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1. May 16, 2016

### fizixfan

The ancient Great Pyramid of Giza had a base of 230.4 meters, and a height of 146.5 meters. A ping pong ball has a diameter of 40 millimeters.

The volume of the Great Pyramid = (b^2 x h)/3 = (230.4^2 x 146.5)/3 = 2,592,276 cubic meters.

The diameter of a ping pong ball is 40 millimeters = 0.04 meters, radius = 0.02 meters, volume = 4/3πr^3 = 4/3 x π x (0.02)^3 = 0.00003351 cubic meters.

Spheres in a pyramidal container take up about 74.05% of the space (been there, done the math - see Thomas Hales' proof of the Kepler Conjecture).

So, the final answer is 2,592,276 / 0.00003351 x 0.7405 = 57,283,807,162, or about 57 billion ping pong balls.

Have I got this right?

2. May 16, 2016

### Staff: Mentor

3. May 17, 2016

### fizixfan

I was using face-centered cubic (FCC) packing - 74.05% of space
If I use random close packing (RCP) of 63.4%, which is perhaps a bit more realistic, I get about 49 billion ping pong balls.

4. May 17, 2016

### Staff: Mentor

Well, if you want realism, the lower balls might get crushed under the pressure...

5. May 17, 2016

### fizixfan

2.7 grams times 49 billion = 132 million kg. I guess the ones near the bottom would get pretty squished.

6. May 17, 2016

### ebos

Sorry but I get a lot less than that unless you first hollowed the pyramid out first. Then it would hold a lot more ping pong balls ; )

7. May 18, 2016

### fizixfan

It was assumed that the pyramid would be hollow