>> Estimate the mass of air in this room.
>
> 3 grams?

Estimate, not guess! You'll never make an Engineer if you can't tell when 
your calculations are off by several orders of magnitude.  BTW a cubic metre 
of air is about 1kg, so you must be in a very small room.

>> Would birds be hotter or colder with fur on their legs?
>
> Presumably this varies depending on the external temperature?

I think it's safe to assume the external temperature is lower than the 
internals of the bird, but anyway the point of this one was that for 
cylinders below a certain radius lagging them actually makes them release 
more heat rather than less, because the surface area increase has more 
affect than the lagging.  Useful to know if you ever think about insulating 
thin pipes :-)

> ...oh, wait, maybe you meant the *graph* of this?

Har har.

> Hmm. Well two cubed is 8, while three squared is 9, so I'm going to go 
> with pi^e being larger.

Wrong!

> Presumably "proving" this would simply involve slightly more arithmetic. 
> :-P

http://mathforum.org/library/drmath/view/53916.html

> quantity. I don't know why it took me so long; it's really quite simple 
> when you look at it. I think I just confused myself too much to see it...

That was the story of my whole thermodynamics course at university!

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