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Old 05-16-2004, 05:34 PM   #21 (permalink)
KnifeMissile
 
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Location: Waterloo, Ontario
I have never understood how this happens. DDDDave, were you not reading this thread? The only reason why this thread went on a philisophical digression is because the question was already answered--and several ways, too! For instance, does this look familiar?
Quote:
Originally posted by fckm
ahh, i see where i went wrong, i did a circumference instead of an area, oops.

hmm, for z in radians, r=radius, x=depth:
z=arcos((r-x)/r)

A=occupied area of the circular end:

A=r^2*z-(r-x)*sqrt(2*r*x-x^2)

where sqrt means square root

and so if V=volume, and L is length of cylinder

V=L*A.

My square root comes from expanding the sine of the arcosine.
Secondly, QED is used to signify the end of a proof. What was your proof, exactly? That you couldn't be bothered to read the thread you're replying to?
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