Friday, October 13, 2006

How Much Of The World's Water Is Contained In A Cow?

This is one of the questions asked by interviewers of applicants for a place at Oxford or Cambridge University. It's claimed that with more and more students obtaining A grades at A-level universities are finding it increasingly difficult to choose between candidates, so make use of 'lateral thinking' questions like the one above.

I wonder if any of the readers of this blog would like to attempt an answer? I can contribute that a cow must hold quite a lot of water, because of the French expression: 'il pleut comme vache qui pisse' (It's raining like a cow pissing).


Alessandro said...

Well, taking the volume of water in the world (is that deliberately ambiguous? What about water stored as steam or superheated liquid under the lithosphere, in the mantle or nearer the core of the Earth?) as 1400 million cubic kilometres, I would convert this to 1400,000,000,000,000,000 cubic metres (1.4 exatonnes).

Now, let us assume (very crudely) that the cow's torso is a cuboid (shocking, I know, but considering that the cow actually has roughly cylindrical torso shape, this will compensate in volume for the legs and head, allowing us to ignore them), dimensions roughly 2.5m long* 1m tall * 1m deep = 2.5 cubic metres. Seeing as a cow is a mammal of a similar order of magnitude to humans, let us say that 60% of its mass (fat inclusive) is made up of water, = 1.5 cubic metres.

And therefore for the final flourish, 1.5/1400,000,000,000,000,000 of the world's water is in a cow; that is roughly one tonne per one exatonne.

Ugly said...

If there are 366 million trillion gallons of water on earth, and 10 gallons of water in a cow (after pissing), then a cow has 2.73224044 × 10^-18% of the Earth's water.

brett jordan said...

If we take this as a word quiz, then 'The World's Water' has 4 letters contained in 'a cow' (w, w, a and o).

Texas Ian said...

If we assume alessandro's estimate of the proportion of the amount of the world's water in cow is pretty close, then we could say that 1.5/1400,000,000,000,000,000 is such a small number and so close to zero as makes no difference.

This being the case I think it is fair to say that there is, in fact, no water in a cow at all!

If you want to get in to Oxford or Cambridge, that's how to do it.

A swede said...

I guess...being not so brilliant in maths...just about a cow-amount...or just the amount that fits in a cow.

marmadont said...

Good point! The question never asked for the proportion of the world's water in a cow, just the amount.

Landak said...

((I find these questions perhaps more interesting than the other fellow commenters on this page - I submitted my application to read Physics at the University of Oxford on Friday! I'm also assuming different dimensions - these are undoubtedly nothing but rough recollections from many a day spent in a field....Take everything with a pinch of NaCl the size of Jupiter!))

Since we are asked how much of the world's water is contained in the cow, rather than what proportion, we can safely ignore any need to calculate the amount of water on this planet - a good thing really, considering there's an awful lot more of the stuff around than that conveniently floating around above the lower-lying areas of the landmass.

We have to build a reasonable model for our cow, in order to be able to easily work out the volume of cow. Let us assume that the cow can be modelled as a cylinder of 2.3m in length, and 0.6m in radius; connected to a sphere of radius 0.1m - that's a gross innacuracy, but hey, the increase width at the base takes into account the decreased width at the snout. Then we have four cylinders of 1m length and 0.075m radius, roughly. We then have to subtract a figure for the lungs for this - cow lungs are larger than humans, and have an overall volume of 3l, and their four stomachs can be roughly discounted, as the higher water content of their contents will roughly-speaking make them equivalent in water-content per unit volume. So, doing the sum:

(4/3*π*(0.1)^3+π*(0.6)^2*2.3+4(π*(0.075)^2))-3 =(5111/6000)π ≈ 2.67611m^3.

Now, the question of "What percentage of the cow is water" is an interesting one. Looking at 'people' - and, I suspect mammals - is a good step to simplify this problem; the only real way to test it is to reduce a sample to ash, and measure how much H2O is given off. Despite the rendering industry doing this periodically with cows, the data isn't easy to come hold of. Different people have different percentages of their bodies made up of water. Babies have the most, being born at about 78%. By one year of age, that amount drops to about 65%. In adult men, about 60% of their bodies is water. However, fat tissue does not have as much water as lean tissue. In adult women, fat makes up more of the body than men, so they have about 55% of thier bodies made of water. Fat men also have less water (as a percentage) than thin men.

So, we assume that the cow is of average weight, and an adult, so we assume that about 60% water content is reasonable. This gives our volume of water as ≈1.60567m^3. Now, because the cow is warm-blooded, the density of the water will be slightly greater than 1tonne/m^3. We assume the cow has a body temperature of 30ºC - a bit hotter than humans, which is "about right" (a cat's normal body temp is 32ºC, iirc). Water at 30ºC will have about a density of 0.99565 g/cm^3, so our mass of water will have a mass of about 1598.68kg, which is a, uh, pretty heavy cow. Like, far to heavy. Bah. This implies a fault in the original dimensions of our model, but I'll continue onwards irrespective! Now, since we know that the molecular weight of water is 18g/mol, we have the total moles of water being *very* approximately equal to 88815.7. Multiply by Avogadro's Number, and get the final answer: About 5.34670764*10^28 molecules of the world's water is contained in the average cow.

Of course, it might be argued that due to the meat-eating society in which we live, and the horrendous inefficiency of biological processes in general, a better measure of "How much water is contained in a cow?" would be a number that represents exactly how much water was required to sustain the cow - how much water was used to irrigate the fields on which his feed grew, how much water was consumed by the farmer and so on. Due to the very damaging nature of Brazilian cattle feedlots to the environment, this measure would probably be an order of magnitude greater than the number of molecules of H2O contained in the cow itself.....

Ken Johnson said...

Well now, that all depends on where is the cow? A cow sitting in Sudan right now doesn't hold much water at all. In fact, it's probably already dead from the effects of the drought. So, your answer is quite simple - for a Sudanese cow "none at all"

Zot said...

I'd guess there are many answers depending on what you choose to focus on. The point of the question is probably to get you thinking, and to see how you choose to interpret it. If you go for the most obvious interpretation without considering alternatives, I'd say you would probably not be likely to succeed.

For instance, my initial thought was that the word "contained" could be interpreted a couple of ways. I mean cows aren't really containers -- water goes in and out of them all the time as they eat grass, give milk, and everything else that cows do. You could argue that none of it is really contained.

You'd probably find that if you could sustain an argument very well, even if it seems a bit odd, you might do quite well in this particular setting...

Anonymous said...

A fair bit if its an ice sculpture of a cow :)

lunicidal said...

Is the cow hollow, like a balloon skin? Is it a average cow or a special breed?

Zac said...

None. It is now the cow's water.

Anonymous said...

I agree with brett jordan said...

I really like these kinds of questions as long as the answer is evaluated by someone with an open mind.
Some tests will mark an answer as wrong if the answer , while correct , isn't the one expected by the test.

When I saw this question , two answers immediately sprung to mind , besides the obvious literal answer (dividing the weight of the water in an average cow (if there is such a thing) with the total amount of water on this planet (which just as with the cow is extremely hard to accurately measure)) :

1) About a cows worth of water
2) No amount of the worlds water is in the cow since that water belongs to the cow.

I see from the comments that others came up with the same answers :)

Instead of an answer you could also go with an Monty Python'esque reply :
"A European or an African cow ?"

AddAnImage said...

The question I'd ask is why? Not being an academic I'm always mistified by the things they consider important... said...

@addanimage : The lesson you learn from a persons answer to these kinds of questions is not, the literal "How Much Of The World's Water Is Contained In A Cow?" , because knowing that really isn't important.
The reason why the question is asked is so you can learn how the person answering the question came to find his answer .. to figure out how he/she thinks.

Another example :
3 students were asked how long it took to cook a turkey in an oven.

The first , calculated the answer using complex physics formula's , taking in account the turkeys weight, massdensity , amount of water, heat from the oven ..etc.

The second went out and bought a turkey , put it in the oven, waited until the turkey was done and then wrote down how long it took.

The third called his mother and asked her.

All 3 students gave the correct answer , but if you could only pick one for a job or a scholarship , which would you choose ?

Zot said...

Yes, that's the point I was trying to make, I agree.

Anonymous said...


Once the water that is in the cow is in the cow and so is not available for consumption by the rest of the global community.

That is unless one discovers a method to tap cows and drain the precious water therein.

B. Mateo

Christa said...

hey whats up?? i know this is very random but my name is christa and im doing a speech on savants because i saw the program on the discovery channel and it amazed me. Personally on your website here i think you should try to draw some of the numbers you see because that would be great if i could see what they looked like. well just a suggestion...get back to me soon please :0)

Bradley Shilling said...

The easiest and most correct answer would be "some" as there is more then none and certainly less then all. However if this is a short answer question you may want to go into more detail though in this case the simplest answer is the path of least resistance so little explanation would be necessary.

Bj said...

The answer is none. No water. Sure, a cow will contain a few gallons of fluids including blood and maybe some milk, but animals do not contain any water per se; it is all saline and serum.

MD said...

Water in a cow is not the world's water, it is the cow's water that has been converted for essential needs. One could argue that you could kill a cow and not get a drop of pure water.

The world's water is the water available in lakes, ponds, seas etc. So the answer to how much of the world's water is contained in a cow is none.

Vanessa said...

I wish I could have written an email instead of a comment but I could not find your email address, if it is even available at all. Anyway...

Hello Daniel. Allow me to introduce myself. My name is Vanessa. I am 18 years old. I'm from North Andover, MA. I saw you on the Science Channel today.. and decided to look for you online. Your story is a very interesting one.

It interests me partly because I have been contemplating the connection between mind and body , the ultimate capacity of each of these (whether there is a limit to their ability, at all), and also the definition of a soul...

And, finally, my interest also stems from my own experience with and odd ability - and the disappearance of it.

I would like to talk with you because I have a couple questions, out of curiousity.

I'm pretty sure that you won't be able to do that because so many people want to talk to you and you are busy busy busy. :)

I am not associated with television or anything like that. And I am not writing a paper for school or the newspaper.

But.. if you can find the time, my email address is

(By the way! You must love the band Sigur Ros if you think Icelandic is such a beautiful language. If you have not listened to the band, I recommend it very much. I, unfortunately, can not understand the lyrics - but I like it very much regardless.)

Hope to hear/read from you.


tom raywood said...

The answer, plainly, is none.

Whatever amount of water is in the cow belongs to the cow, not to the world.

Anonymous said...

Only the O as in H2O HaHa

Robert said...

Christa said...
hey whats up?? i know this is very random but my name is christa and im doing a speech on savants because i saw the program on the discovery channel and it amazed me. Personally on your website here i think you should try to draw some of the numbers you see because that would be great if i could see what they looked like. well just a suggestion...get back to me soon please :0)

10:38 PM I totally agree with Christa's suggestion and must commend her for reading my thoughts prior to their conception. Robert

John Pozadzides said...

Although I am from Texas, I’m no cow expert :-), nor am I a gifted mathematician, but I believe I have a solution to the question at hand.

First, the words "The World's" are clearly meant to throw everyone off… If we apply a little conservation of words here, the real question is simply "How much water is in a cow?"

Well, if you give me the following, I'll tell you within about an ounce:

- A sacrificial cow.
- A cow-sized scale.
- A very clean incinerator with a cow-sized opening.
- A small bag to contain the ashes.
- A small scale to weigh the ashes.

Since water weights 8 pounds per gallon, it seems to me that all we need to do is remove the water.

The difference between the before and after weight should give us an exact figure.

Of course, it would be a shame to waste all that tasty hamburger!


Anonymous said...

I like bj's answer (none, because it's not water). also make a good point (not as Pythonesque as it first seems) cows vary, Bos torus or Bos indicus etc. Most of the bovine population is in Africa and India but Western cows are better fed.

Interestingly most people seem to overestimate the size of a cow. There is of course tremendous variation, but Milkers (e.g. Holsten Fresians tend to be the largest at about 5-600Kg, beef cattle in the UK and US usually average 400Kg, of which 1/3 is edible. The largest of bulls are just over a ton.

When I won my scolarship to Cambridge (Natural Sciences) in 1978. I do remember the interview as being quite gruelling, but sadly I don't remember being asked any interesting questions like this to break the ice - pity. But I think I managed a reasonable showing in the maths paper "if it takes 24 hours to defrost a frozen turkey, how long would it take to defrost a frozen Siberian mamoth".

If we take it literally and avoid the obvious philosophical points, then the temptation is to answer simply (say) 500kg x (say) 65% water content = 325 L. This is of course the wrong answer since it avoids lots of interesting side issues. I have also seen the question rendered as "is contained in the cow". This is far more sensible since one would presumably have the ability to judge size, condition and specifically hydration levels of the specific beast in quetsion. You could also imply this meant all cows, so we can discuss relative levels of meat and milk consumption to deduce the global bovine population (1.5 x 109 if you must know). Then there is the issue of proportion and how much water there is in the world inc atmoshperic and underground reserves.

So all in all this is an excellent mental workout and no doubt demonstrates why Cambridge is the superior institution.