PLEASE CHECK THIS OUT. Our own Aeronmelon is going through some shit at the moment and could use some help. Check it out here and consider an upvote or a comment to push it into activity. Sorry, not something I do often or will be spamming. But I care about my friend and if I can get a couple more eyes on his situation then I'm going to try to do what I can.
The area is very easy to calc, its only adding clear poligons, basic geometry. Somewhat harder to calculate the volumen of this thing.
Your spanish is leaking, mate.
Fun: The leak looks the same as if it had sprung from german!
Volume is also nothing but polygons, where accuracy depends on number of slices.
Or: dump it in a water tub and measure height of water line.
Yeah, the easy way, but not so easy with pen and paper (also only basic math, but a lot)
Hard to say if the integral can be solved analytically or not.
It's not hard to say at all, "if the integral can be solved analytically or not" is hardly a tongue twister
Try "she sells sea shells by the sea shore." Now that's hard to say