Ann in Houston wrote:

A five gallon water jug is much bigger than one
square foot.

You mean, "cubic" foot. And it isn't. I just did a rough calculation
(using a sheet of 8.5"x11" paper to measure a 5gal jug because i didn't
have a ruler or tape measure).

The jug is 10" in diameter and 14" tall. The volume of a cube is
Length*height*width=1728 cubic inches for a 1' cube. The volume of a
cylinder is Pi*Radius*Radius*height= Pi*5*5*14=1100 cubic inches. Not
surprisingly; smaller than a 12" cube. :-)
--
derek

"Derek Broughton" wrote in message
...
Ann in Houston wrote:

A five gallon water jug is much bigger than one
square foot.

You mean, "cubic" foot.
oops! sorry - I did mean cubic.

snip


The jug is 10" in diameter and 14" tall. The volume of a cube is
Length*height*width=1728 cubic inches for a 1' cube. The volume of a
cylinder is Pi*Radius*Radius*height= Pi*5*5*14=1100 cubic inches. Not
surprisingly; smaller than a 12" cube. :-)
--
derek

Well, okay. I can't argue the facts since you went to the trouble to measure
it. It sure seemed close, though. I know that the water bottle also is
sort of cone shaped at the bottom. Do your calculations treat the bottle as
a full cylinder, or did you stop at the top of the neck? That could make a
real difference too. Thanks for being intrigued enough to check it out.

Ann in Houston wrote:

The jug is 10" in diameter and 14" tall. The volume of a cube is
Length*height*width=1728 cubic inches for a 1' cube. The volume of a
cylinder is Pi*Radius*Radius*height= Pi*5*5*14=1100 cubic inches. Not
surprisingly; smaller than a 12" cube. :-)


Well, okay. I can't argue the facts since you went to the trouble to
measure
it. It sure seemed close, though. I know that the water bottle also is
sort of cone shaped at the bottom. Do your calculations treat the bottle
as
a full cylinder, or did you stop at the top of the neck? That could make
a real difference too. Thanks for being intrigued enough to check it out.

I treated it as an exact cylinder - if I wanted to figure out the difference
due to curvature, I'd actually have emptied the contents into a proper
measuring container, as otherwise I'd have to take into account the
curvature on the bottom, the tapering on the top, the size of the neck (at
least, the one I used had some water in the neck), and the thickness of the
plastic (which looks like it probably isn't even uniform). It's a lot
easier to make assumptions :-) (besides which, since I couldn't get an
exact measurement, it was all rough anyway). In fact, either our water
supplier is cheating us, or the jug is actually a little bigger than my
calculation, because it should really be about 1150 cu.in. for a 5 (US)
gallon container.
--
derek

Ann in Houston wrote:

Do your calculations treat the bottle
as
a full cylinder, or did you stop at the top of the neck? That could
make
a real difference too. Thanks for being intrigued enough to check it
out.

I treated it as an exact cylinder - if I wanted to figure out the
difference
due to curvature, I'd actually have emptied the contents into a proper
measuring container, as otherwise I'd have to take into account the
curvature on the bottom, the tapering on the top, the size of the neck (at
least, the one I used had some water in the neck), and the thickness of
the
plastic (which looks like it probably isn't even uniform). It's a lot
easier to make assumptions :-) (besides which, since I couldn't get an
exact measurement, it was all rough anyway). In fact, either our water
supplier is cheating us, or the jug is actually a little bigger than my
calculation, because it should really be about 1150 cu.in. for a 5 (US)
gallon container.
--
derek

I certainly wouldn't have bothered to figure out the neck and all. The real
question was whether or not 12 cubic inches could hold 7.5 gallons. I
appreciate you doing it the way you did.

"Ann in Houston" wrote:
I certainly wouldn't have bothered to figure out the neck and all. The real
question was whether or not 12 cubic inches could hold 7.5 gallons. I
appreciate you doing it the way you did.

nitpick on
It's 1728 cubic inches (12*12*12 - a cube 12 inches in all three dimensions),
not 12 cubic inches.
nitpick off

Now, anyone want to talk about koi or something? ;-)

On or about Thu, 18 Nov 2004 21:52:58 GMT, "Ann in Houston"
wrote something like:

I certainly wouldn't have bothered to figure out the neck and all. The real
question was whether or not 12 cubic inches could hold 7.5 gallons.

Only if 231 cubic inches can hold one gallon.
--
Crashj

Ann in Houston wrote:

I certainly wouldn't have bothered to figure out the neck and all. The real
question was whether or not 12 cubic inches could hold 7.5 gallons. I
appreciate you doing it the way you did.




231 cu in per gal, not 12

12"x12"x12"= 1728 cu in = 1 cubic foot = 7.5 gal capacity.







--
http://www.kencofish.com Ken Arnold,
401-781-9642 cell 401-225-0556
Importer/Exporter of Goldfish,Koi,rare Predators
Shipping to legal states/countries only!
Permalon liners, Oase & Supreme Pondmaster pumps


$9.95 internet access https://sub.copper.net/promo/5339894.asp

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sending of this contaminant free message We do concede
that a signicant number of electrons may have been
inconvenienced

KenCo wrote:

Ann in Houston wrote:

I certainly wouldn't have bothered to figure out the neck and all. The real
question was whether or not 12 cubic inches could hold 7.5 gallons. I
appreciate you doing it the way you did.

231 cu in per gal, not 12

12"x12"x12"= 1728 cu in = 1 cubic foot = 7.5 gal capacity.

As Ken pointed out:

12 cubic inches is not a 12 inch cube. BIG difference.

12 cubic inches is a 2.29 inch cube.

A 12 inch cube is 1728 cubic inches.

--
Pardon my spam deterrent; send email to
Cheers, Steve Henning in Reading, PA USA
http://home.earthlink.net/~rhodyman

KenCo wrote:

Ann in Houston wrote:

I certainly wouldn't have bothered to figure out the neck and all. The real
question was whether or not 12 cubic inches could hold 7.5 gallons. I
appreciate you doing it the way you did.

231 cu in per gal, not 12

12"x12"x12"= 1728 cu in = 1 cubic foot = 7.5 gal capacity.

As Ken pointed out:

12 cubic inches is not a 12 inch cube. BIG difference.

12 cubic inches is a 2.29 inch cube.

A 12 inch cube is 1728 cubic inches.

--
Pardon my spam deterrent; send email to
Cheers, Steve Henning in Reading, PA USA
http://home.earthlink.net/~rhodyman

Derek Broughton wrote:
I treated it as an exact cylinder - if I wanted to figure out the difference
due to curvature, I'd actually have emptied the contents into a proper
measuring container, as otherwise I'd have to take into account the
curvature on the bottom, the tapering on the top, the size of the neck (at
least, the one I used had some water in the neck), and the thickness of the
plastic (which looks like it probably isn't even uniform). It's a lot
easier to make assumptions :-) (besides which, since I couldn't get an
exact measurement, it was all rough anyway). In fact, either our water
supplier is cheating us, or the jug is actually a little bigger than my
calculation, because it should really be about 1150 cu.in. for a 5 (US)
gallon container.

Assumptions make for easier math for sure, but with a little calculus and
angle measurements and the like you could calculate it precisely. I mean
if you wanted to take the time that is. No need for emptying and filling
or calibrated measurements of volume that way. Just a precise mathematical
description of your container and some number crunching. But for general
purposes particularly when it comes to fish, I agree, making assumptions
or rounding a bit usually is okay. Just don't make too big of assumptions
if dealing with something like medication.

As to the OP, if you are having trouble conceptualizing the cubic foot
holding 7.5g of water, look at a standard 5.5g and 10g aquarium. A 5.5g is
about 16" x 8" x 10" ~= 0.75 cubic feet. A 10g is 20" x 10" x 12" ~= 1.39
cubic feet. The reason the 5g water jug looks bigger than the 5.5g tank is
just dimensions. It's tall and narrow with a big dent for the handle (at
least with my water company), which gives the impression of being bigger
than a cubic foot. I seem to remember reading a study where humans thought
a tall, narrow item held more when compared to an equal volume sized
short, round item. I believe the study was related to overeating due to
underestimating the volume of what one was consuming, but not positive.

"Cichlidiot" wrote in message
...
Assumptions make for easier math for sure, but with a little calculus and
angle measurements and the like you could calculate it precisely. I mean
if you wanted to take the time that is. No need for emptying and filling
or calibrated measurements of volume that way. Just a precise mathematical
description of your container and some number crunching. But for general
purposes particularly when it comes to fish, I agree, making assumptions
or rounding a bit usually is okay. Just don't make too big of assumptions
if dealing with something like medication.

Sure you could use triple integrals to calculate the volume of an
irregularly shaped object, but the fact is those of us that took calculus
would probably have to crack open our text books to remember how, since it's
not a concept that is used frequently. Additionally according to the US
Census only 24.4% of America holds a bachelors or greater, and bear in mind
many degrees do not require exposure to higher levels of math.

Finally the original poster was not questioning the math or the conversion
ratios, but expressing difficulty in visualizing how a 5 gallon jug was less
than 1 cubic foot.

References:
http://factfinder.census.gov/servlet...SF3_U&-_sse=on

Snooze wrote:
Sure you could use triple integrals to calculate the volume of an
irregularly shaped object, but the fact is those of us that took calculus
would probably have to crack open our text books to remember how, since it's
not a concept that is used frequently. Additionally according to the US
Census only 24.4% of America holds a bachelors or greater, and bear in mind
many degrees do not require exposure to higher levels of math.

I'll admit that I am more mathematically inclined than most (after all, I
took calculus in high school, completed my AP test in 30 mins getting a 5
and took calculus 3/C for fun in college). However, there are computer
programs which aid those less mathematically inclined should they desire.
I was just pointing out that there are methods other than estimations or
pouring x volume amounts to calculate the exact volume. Calculations that
were probably behind the design of the 5g water bottle.

Finally the original poster was not questioning the math or the conversion
ratios, but expressing difficulty in visualizing how a 5 gallon jug was less
than 1 cubic foot.

I believe I covered that in the second paragraph of my reply, which you
did not quote, when I explained the perceptual bias people have when
estimating the volume of tall, narrow containers compared to shorter
containers of equal volume. Even though I know otherwise, when I put my 5g
water bottle next to my 5.5g tank, the bottle "looks" bigger. It's just a
perceptual bias, perhaps related to other optical illusions regarding
size. I suppose what one can draw from this is that when in doubt, carry a
ruler, heh.

"Cichlidiot" wrote in message
...
I'll admit that I am more mathematically inclined than most (after all, I
took calculus in high school, completed my AP test in 30 mins getting a 5
and took calculus 3/C for fun in college).

Wow! Bragging about high school AP scores, what do you think this is?
usenet? *sarcasm*

Snooze