Without using a bathtub of water, how would i calculated the volume of
my body in cubic centimetres?

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Request for Question Clarification by redhoss-ga on 05 Jan 2006 17:25 PST

Is this a purely theoretical question or do actually want to do it. Is
cost of the method of any concern.

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Clarification of Question by checatelo-ga on 06 Jan 2006 01:38 PST

I am intending to do it, but with as little expense as possible. I
wondered if there was a mathematical model that can be applied to the
problem and then practically applied.

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Request for Question Clarification by richard-ga on 12 Jan 2006 06:53 PST

Be sure to read mikewa-ga's comment.
Well done!

A bathtub of beer will do nicely.

There are a couple of ways.  I expect a full body scan would produce
results that allowed volume calculation.  There are also projection or
screening methods for precisely fitting clothes or for some medical
work that would probably also do the trick.
But I like Paf's suggestion better, which has the advantage that you
could do some experiments:  drinking some of the beer and seeing if
the level goes down or remains the same.  In theory, it should remain
the same, since your belly should expand by the same volume that you
remove from the tub.  But maybe there are air cavities that get
compressed instead; or maybe co2 is released by drinking and expands
your belly more.  We've really got to try this.  ;-)

The problem with using liquid bath or immersion is there would be
errors if you pee or swallow some of the water, or beer. If you don't
drink beer then the error would be minimal because you would return
the beer to the bath by involuntary reaction.

So you may try casts or moulds. Depending on many factors, allergy and
eagerness of those who'd cast your naked body among them, you can
choose plaster-of-Paris, chalk, paper mache, fiberglass and resin,
pure portland cement with water, reinforced concrete, or vacuum seal
using hard enough plastic that can retain your body shape when cut in
half.
Oh, yes, air pockets are possible errors too, so the vacuum seal might
be preferable for you.

Then use water or beer to fill up the resealed cast/mould to get the
volume of your body plus the volume of covers, if you used them.

'Nother idea:  Find out your specific gravity by getting under water
in a swimming pool:  how much additional weight is needed to hold you
in equalibrium under water; or how heavy you still are when submerged
in water.  Then weigh yourself and apply the plus or minus factor for
your specific gravity.
For example:  back when I was fit, I was heavier than water - sank
when I expelled air from my lungs -  so my body volume was slightly
less than the volume of water that weighed as much as I did.

You've just replaced a bathtub of water with a swimming pool...hardly
a step in the right direction!

You could try to integrate yourself (kinda...)
Imaging cutting yourself up with planes parallel to the floor.  You
can approximate these cuts as ellipses (or 2-3 ellipsis in the case of
your arms/legs).  You can find the height and length of the ellipses
by tracing yourself with chalk on your stomach, then on your side
(additional info may be needed for your arms.

The prescision depends on how many cuts you decide to make, this
depends on how much time you feel like spending...

Find the area (2D) of each cut (pi*width on side*width on stomach). 
You can then use an integral approximation method to find the volume.

I know I was less than explicit in the mathy sections of this
explanation...but I just don't have the time...If someone would be
kind enough to finish my thought it would be much appreciated.

-Fractl

Consider a small airtight room of known volume.  You are in the room
and the airpressure can be precisely measured.  If you add a known
volume of air at a known pressure to the room, you can then measure
the resulting increase in air pressure in the room.  Then calculate
what the increase in air pressure would have been if the room had been
empty.  It will be less.  This is enough to calculate how much less
space was in the room when you were in it (i.e. your volume).

How much less empty air space.

Fractl, 
I knew that I should have anticipated that complaint, but I was more
interested in suggesting an alternative method (that might even work
:).  Okay, we also have to compensate for the specific gravity of
chlorinated water.
What you are suggesting is about what a spin tomography would produce,
probably the most accurate and realizable solution  - at a price.

Anse1001 suggestion is also interesting.  Who knows, maybe NASA has a
facility that could do that.

Checatelo, 
Your clarification:  The bathtub still seems to be the easiest and
best way to do it.  Just fill the tub, get in, and with everything
under water mark the level.  Then get out and weigh yourself sopping
wet to compare with your dry weight.  And then fill the tub to the
level marked using a measuring vessel.
Add the difference of your weights for the water that you removed.
I wish you succes, Maoarin

This might be of interest:

http://www.newton.dep.anl.gov/askasci/gen01/gen01048.htm

A bathtub of beer would tickle!  All those little bubbles running
across your whole body... LOL!  You'd never be able to measure the
water level because your laughter would keep the tub sloshing!

Gotta go - time to wash my face with vodka and brush my teeth with bourbon.

I would do it the ol' dip my body in the bath tub technique but my
bath isn't big enough to do this.

Talk to your neighbors, maybe one of them would like to help, or take
a room in a hotel with big tubs.

For a start, just how accurately do you need the answer? If you are
not too picky you can get an estimate quite quickly. Since most people
are close to neutral buoyancy then you weigh 1kg/litre. So, simply
multiply your weight in kg by 1000 to get your volume in ccs.
Beyond that, back to the bathtub. I am not clear why you reject this
solution, it is both fast and accurate

Its not an overly complex problem, consider the volume of any
individual. It is not a consistant volume, as when you breathe, your
chest comes out, when you work out, your muscles take up a much larger
space, if you eat a big meal, your pants suddenly become tight.. im
sure the point here is obvious, that accuracy is not an important
issue.

expansion on mike-wa's
if you are x% water, then you must be y% not water, where x% + y% =
100% (so cleaver)
I am sure that there is a detailed breakdown of what that y% is likely
to be made up of, and the appropriate calculations could easily be
made.

With the tub of water method, dont take a breath, because then you
will displace the same amount of water as the volume of air you
inhaled. So dont take a breath, or.. stick with my expansion of
mike-wa's idea so you dont drown.

Beer is deliscious.

Thanks for your comments. The initial thought that spurned this, was
if I was made of Plasticine how small a cuboid could I be squashed
into. I guess I could just do a moulding cast and fill it in with
plasticine, and find out. Anyhow, at the risk of sounding highly
silly, I weigh 70kg so if I times that by 1000 (as suggested by
mikewa-ga) = 70,000 ccs (what does ccs stand for cubic such and such)
how would you convert that figure to centimetres squared? Feel free to
patronise me on the basis that I have now shown you my illiteracy to
certain math related problems hehehe. Thanks

ccs = "cc"s
cc stands for cubic centimeters, so 70,000 is your answer (I figure
your request for it in square centimeters was a typo...2D vs. 3D and
all)

70,000 cm^3
=   .7 m^3
=   70 litres
= 2.47 ft^3
= 18.5 Gal.
=    1 mushed up cube of plasticine checatelo


-Fractl

Well, it is not 0,7 cubic meter (that would be 700 liters), but
Right, 70,000 cc = 70 liters.  That is about enough to cover a square
meter (3.3 ft) 7 cm deep, that is less than 3 inches.
How would you liked to be packaged, squashed like that, or in a cube: 
about 16+ inches on the edges (bad for back, legs, head)?

For a while I was worried that you didn't fit in a bathtub, but now -
70 kilo - it really should be possible to fold yourself up below the
rim, if not below the overflow drain.

Chears, Myoarin

I like 's answer:
"For a start, just how accurately do you need the answer? If you are
not too picky you can get an estimate quite quickly. Since most people
are close to neutral buoyancy then you weigh 1kg/litre. So, simply
multiply your weight in kg by 1000 to get your volume in ccs.
Beyond that, back to the bathtub. I am not clear why you reject this
solution, it is both fast and accurate"

But to extend it - it would be interesting to know how the above
methoid relates to the waist-line measurement and height (W and H,
say).

Although we are NOT a cylinder,I would expect the volume to be some
fixed proportion of pi*H*W^2. , which is the volume of the cylinder.
Given W, H and X=mass for a sample of individuals, we could check the
model of constant-proportion. The constant may differ for different
'shapes' of people - e.g. by sex and podginess factors.

If anybody tries this - please let me know the outcome!

Thanks

JOHN BIBBY  (York, England)