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

In summary, the Great Pyramid of Giza, with a base of 230.4 meters and a height of 146.5 meters, has a volume of approximately 2,592,276 cubic meters. The volume of a ping pong ball, with a diameter of 40 millimeters, is 0.00003351 cubic meters. Using the face-centered cubic packing method, the pyramid could hold about 57 billion ping pong balls. However, using the more realistic random close packing method, it could hold about 49 billion ping pong balls.
  • #1
fizixfan
105
33
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?
 
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  • #3
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
Well, if you want realism, the lower balls might get crushed under the pressure...
 
  • #5
2.7 grams times 49 billion = 132 million kg. I guess the ones near the bottom would get pretty squished.
 
  • #6
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
ebos said:
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 ; )

It was assumed that the pyramid would be hollow o_O
 

1. How can you calculate the number of ping pong balls that would fit into the Great Pyramid?

To calculate the number of ping pong balls that would fit into the Great Pyramid, we would need to know the volume of the pyramid and the volume of a single ping pong ball. We can then divide the volume of the pyramid by the volume of a ping pong ball to get an estimate of the number of balls that would fit inside.

2. What is the volume of the Great Pyramid?

The volume of the Great Pyramid is approximately 2,583,283 cubic meters. This value can vary slightly depending on the source and method of measurement used.

3. What is the volume of a ping pong ball?

The volume of a standard ping pong ball is approximately 2.7 cubic inches or 0.000044246 cubic meters. Again, this value can vary slightly depending on the specific brand or type of ping pong ball.

4. Can you provide an estimate of the number of ping pong balls that would fit into the Great Pyramid?

Based on the volume of the Great Pyramid and the volume of a ping pong ball, we can estimate that approximately 6.6 billion ping pong balls would fit inside the pyramid. However, this is only an estimate and may not be an accurate representation due to the irregular shape of the pyramid.

5. What other factors could affect the accuracy of the estimate?

Aside from the irregular shape of the pyramid, other factors that could affect the accuracy of the estimate include the size and shape of the ping pong balls, the presence of any obstacles or structures inside the pyramid, and the measurement methods used for both the pyramid and the ping pong balls.

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