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Q: Mathematics ( Answered 5 out of 5 stars,   3 Comments )
Subject: Mathematics
Category: Science > Math
Asked by: jobbie-ga
List Price: $10.00
Posted: 26 Aug 2002 20:19 PDT
Expires: 25 Sep 2002 20:19 PDT
Question ID: 58891
How many ping pong balls could be placed in the total internal volume
of a 747 airplane?
Subject: Re: Mathematics
Answered By: mwalcoff-ga on 26 Aug 2002 21:00 PDT
Rated:5 out of 5 stars
According to Boeing, a 747-200 or 747-300 has a carrying volume of
26,600 cubic feet (
A 747-400 has a passenger interior volume of 31,295 cubic feet

A ping pong ball is 3.77 cm, or 1.48 inches, in diameter, according to
( We'll conceptualize
each ping pong ball as a cube of 1.48"x1.48"x1.48", or 0.001876 cubic
feet, to account for the empty space between the spherical balls. I
used ( to convert cubic
inches to cubic feet; there are 1,728 cubic inches in a cubic foot.

Divide 26,600 by 0.001876, and you get 14,179,104 ping pong balls that
could fit in a 747-200 or 747-300.

Since the 26,600 cubic feet number probably does not include the
cockpit, I looked up the cockpit's size. According to
( -- yes, there is a Web
page for everything -- a 747's cockpit is about 14'x15'x8', or 1,680
cubic feet. That's another 895,522 ping pong balls.

Add 14,179,104 and 895,522 and you get 15,074,626 ping pong balls in a

I hope this answer meets your needs. Please do not hesitate to request
clarification if needed.

Search strategy:

747 airplane cubic feet

ping pong ball diameter


747 cockpit dimensions

Request for Answer Clarification by jobbie-ga on 26 Aug 2002 21:27 PDT
Dear Expert,  I am a first time user of this service and am amazed at
the speed in which you addressed my question.  I thank you for this
pleasant "first time" experience.  I am looking for the total volume
of a Boeing 747 for total internal volume.  I guess if you took out
the seats, navigating equipment and just focused on the total internal
volume it would not longer be a Boeing 747.  Or is there a simple
answer to finding total internal volume of a 747?  Again thank you for
the research that you have already done.  Respectfully, Jobbie-ga

Clarification of Answer by mwalcoff-ga on 26 Aug 2002 22:56 PDT
Thank you for the compliment on the answer.

I suppose the answer to your follow-up question depends on what
exactly you are thinking of. The figure of 26,600 cubic feet refers to
a 747 designed for transporting cargo. Thus, it would be pretty empty
except for the cockpit and equipment. The figure would not include
parts of the plane irrelevant to cargo transportation, such as the
wings, engines, etc.

The 31,295 cubic feet figure for the 747-400 refers to the size of the
passenger interior. I guess you would have to take out the seats and
storage bins to reach that volume figure.

If you want to know how many ping pong balls could fit into the plane
without taking out any of the seats or bins, I don't know quite how to
figure that out. Sorry.
jobbie-ga rated this answer:5 out of 5 stars
I am certain that my list price had something to do with the timely
response to my question.  This was a valuable "first time" experience
for me.  With enthusiasm I give this researcher 5 stars.  Jobbie-ga

Subject: Sphere packing
From: ulu-ga on 27 Aug 2002 01:01 PDT
You might want to look at this prior answer.  It suggests a correction
factor to get the maximum packing:

(packing density)*(Cube volume)/(Sphere volume)
= pi/(3*sqrt(2)) * (d^3) / (4/3*pi*(d/2)^3)
= sqrt(2)
= 1.414213562...

So 21,318,740 would be the adjusted figure.

But that number is too high because that packing density assumes it is
surrounded by other ping pong balls.  It would be less efficeint in
contact with flat surfaces.  I can't do that calculation.

Thank you for making Google Answers your airline of choice.

So where are you flying all these ping pong balls?  :-)
Subject: Re: Mathematics
From: mwalcoff-ga on 27 Aug 2002 08:19 PDT
That's a good point. I was assuming we were stacking the balls as such:
o o o o o 
o o o o o
o o o o o
o o o o o
o o o o o

But you could more efficiently stack them like this:
o o o o o 
 o o o o o
o o o o o
 o o o o o
o o o o o
Subject: Re: Mathematics
From: tne-ga on 27 Aug 2002 16:37 PDT
If crushing is llowed you could probably stack them like this



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