KnifeMissile

Okay, I will now agree with CSflim's formula, as convoluted as it is. I have an alternate formula (using different choices of identities) and will display both his and mine for comparison (not that mine's any simpler)...

If x is the depth, r the radius and L the length, then the volume V is:

V = L*r² * ( arccos((r-x)/r) - sin( 2*arccos((r-x)/r) )/2 )
V = L*r * ( r*arccos((r-x)/r) - 2(r-x)*sin( arccos((r-x)/r) ) )

or, you can simplify it in a two step formula:

z = arccos((r-x)/r)
V = L*r² * ( z - sin( 2*z )/2 )
V = L*r * ( r*z - 2(r-x)*sin(z) )

Ah, isn't arcos nice...


So, what were those two formulas, again?