3-Dimentional lens volume formula

[Rogue_Forge]

I made this formula to calculate the volume of a 3-dimentional lens shape and wondered where I should put it, should I make a page for it? its a pretty useful formula cause other calcs just combine multiple shapes to look like a 3D lens cap for calcs

https://vsbattles.fandom.com/wiki/U...ate_the_Volume_of_a_3-Dimentional_Convex_lens

 

[Rogue_Forge]

Bump

 

[MeiouHades]

Generally for something like this you'd set up an integral to calculate the area under the parabola, then multiply that by the height of the lens (assuming it's "flat" on the side, if not then that is more complicated) and then multiply that by two. Alternatively you could set up two integrals and subtract the areas and then multiply it by the height, the result is the same. The reason I suggest instead of your formula (which is actually correct) is because it's much more generalized (essentially allows you to calculate area under some smaller part of the parabola), your formula is only true for max area (that is, when height is maximized) but that may not always be the case for every calc, so this approach has more applications. Although technically both height and the base are covariant so it may not seem like it matters but I do prefer being more thorough.

 

[Rogue_Forge]

Generally for something like this you'd set up an integral to calculate the area under the parabola, then multiply that by the height of the lens (assuming it's "flat" on the side, if not then that is more complicated) and then multiply that by two. Alternatively you could set up two integrals and subtract the areas and then multiply it by the height, the result is the same. The reason I suggest instead of your formula (which is actually correct) is because it's much more generalized (essentially allows you to calculate area under some smaller part of the parabola), your formula is only true for max area (that is, when height is maximized) but that may not always be the case for every calc, so this approach has more applications. Although technically both height and the base are covariant so it may not seem like it matters but I do prefer being more thorough.

I think I saw a formula for what you are talking about but I cant really tell

The formula is V=(1/3)πh^2(3R - h) for each cap where the volume of a convex lens is the sum of the volumes of its two spherical caps

I'm pretty sure this is for 3-Dimentional convex lenses with rounded sides (although I could be wrong)

Also the main reason I made this calc was cause of this feat which doesn't seem to have any curve on the side (although that could be due to the weird angle)