Thursday, May 14, 2009

Ping Pong Balls

The other day I posted a twitter tweet asking the question:

What would be the required diameter of a six foot tall cylinder in order to hold 1,000 ping pong balls?

Pretty quickly a member of our Grace family responded on my facebook page (thanks Ed):



1.575 in = D of a ping pong ball

V = 4/3 * 3.14 * r^3 4/3 * 3.14 * .7875^3 = 2.045 in^3

2.045 in^3 * 1000 balls = 2045 in^3

Spheres have a theoretical packing efficiency of 74% against themselves so

2045 in^2 74
_________ = _______
x 100

(2045 * 100) / /74 = 2763 in^3

2763 in ^ 3 = 3.14 * r^2 * 72 inches

12.22 in^2 = r^2 r = 3.50 inches

Diameter of 7.0 inches

But, this really breaks down, because this assumes 100% efficiency of the spheres against the cylinder walls. As the cylinder walls get smaller, the packing efficiency breaks down big time. so, realistically it would probably be around 10 inches or so.

To get the best answer, you would need to figure out the minimum size of a circle that could hold 22 1.575 diameter circles.



The response reminded me:

1. Communication is increasingly varied. The question posed on twitter was answered on facebook and is now being shared with you by email.

2. People with so many different gifts make up the family of Grace and each gift has a part to play in advancing the Kingdom of Heaven.

The Kingdom needs people who are great at:

  • Teaching
  • Organizing
  • Singing
  • Encouraging
  • Welcoming

And thousand of other activities (including calculating the diameter of a cylinder to hold 1,000 ping pong balls.)

When they all come together, empowered by God, earth becomes a little more “as it is in heaven” and the Kingdom is advanced!

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