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.
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